When I was 23, I tell Stuart Donaldson, the newly elected member of parliament for West Aberdeenshire and Kincardine, I had difficulty getting out of bed and putting my clothes on the right way round. “Well, yes, sometimes, it can be a bit of a challenge,” he says.

Stuart Donaldson is 23, and his new job as an MP has come as a bit of a shock to everyone, not least his girlfriend. “We met at uni, and she started going out with this guy who would sleep all day and not do much else, and would miss all his lectures. For her to suddenly now be with this guy who’s an MP at 23… it’s quite mad.”

It is quite mad. Donaldson is one of the new SNP MPs, and in any ordinary political landscape he would have been an out-and-out no-hoper – he had a 17,000 majority to overturn, and the SNP didn’t even come second in his constituency last time. And yet here he is, in Portcullis House, the building across the road from Westminster that’s home to many MP offices, on one of the hottest days of the year, sweating away in a suit he’s clearly not used to wearing.

His original plan was to go to China and work for a tour company. Instead he’s entered parliament, by what seems almost like accident. This has its swings and roundabouts. On the one hand, he’s landed perhaps the best graduate salary ever. That must be quite nice, I say. “It’s actually a bit overwhelming,” he says. “I’ve suddenly got all this money. I’m not sure what to do with it.” On the other, he’s struggling to adapt to a whole new climate. “It has never been as hot as this in Scotland, ever.”

Stuart Donaldson.

Then: ‘Sleeping all day’ at university.

Now: MP for West Aberdeenshire & Kincardine.

And… He is 23 years old.

Photograph: Katherine Anne Rose for the Observer New Review

I like Donaldson. How could I not? He’s so unassuming and unpolitician-like, and keeps saying the kinds of things I imagine would cause most spin doctors to have a cardiac event. And as much as I’d like to patronise him – he’s only a couple of years older than my nephew, who I’m not sure I’d trust to run a bath let alone the country – it becomes clear when I speak to him that he won his seat through a combination of hard graft and a very clever and effective grassroots campaign. And, of course, the massive tidal wave of popularity for the SNP that took everyone by surprise, not least the SNP.

Kirsten Oswald, the new member for East Renfrewshire, tells me they joke about the people who popped out for a pint of milk in January and came back as MPs, and it’s not far off what actually happened. She wasn’t even a member of the party a year ago. The incredible success of Nicola Sturgeon and the SNP turned out to be the story of the 2015 election, and the result is a massive new influx of 56 SNP MPs, up from just six in the last parliament, and lone, embattled representatives for each of the Scottish Labour, Conservative and the Lib Dem parties.

All over Westminster I find natural redheads and strawberry blonds with pale, freckled skin reddening in the sun. “It’s an extremely difficult place to get to grips with,” Toby Helm, the Observer’s political editor tells me. “It’s like entering the weirdest boarding school ever. These days you see them hanging around in small groups and hear Scottish accents far more often about the place. They are clearly quite enjoying it. But it is an extraordinary thing they are trying to do. They want to appear like they are playing a constructive part in parliamentary life at Westminster while really what they are plotting is to torpedo the union and break free of Westminster altogether.”

Tommy Sheppard.

Then: Comedy club owner.

Now: MP for Edinburgh East.

And… ‘If you said to me a year ago I’d be an SNP MP, I’d have denied both parts of that proposition,’ says Sheppard.

Photograph: Katherine Anne Rose for the Observer New Review

Because, of course, Westminster, and everything it stands for, is essentially their worst nightmare. And yet here they are now, part of it. What’s it like, I ask Tommy Sheppard, the new member for Edinburgh East, being in the belly of the beast? Isn’t this – and I wave my arm across a stupendous view of the palace of Westminster and the Thames – everything you stand against?

“Well, yes. By any test of what a modern, democratic government is, this place is a shambles. It’s a cross between a museum and a pantomime.”

Sheppard is another unlikely member of the SNP benches. He’s the owner of the Stand comedy club in Edinburgh and was previously a hardcore Labour activist. And, like a huge swath of Scotland, his conversion to the nationalist cause only happened about three minutes ago. “If you’d said to me a year ago I would be an SNP MP, I’d have denied both parts of that statement.”

I know the SNP needs to play this up for the Scottish crowd back home, but he has a point about the place. I’m not a political reporter. I’ve never worked in the lobby. I’m just Ms Average who has spent two days hanging around the Palace of Westminster, and I can safely report that it is a ridiculous place. There’s no getting away from it. Given the £7bn estimate to renovate it, I’m now converted to the idea that it should be turned into a luxury hotel, and a new building modelled on a Travelodge should be built in somewhere like Bolton. The doormen wear black tie and tails, and whichever way you look there’s somebody in a gold brooch and chain for no discernible reason. And then there’s prime minister’s questions, which makes most lay people want to give up their passport and leave the country.

“That’s the worst,” Philippa Whitford tells me. “I sit there thinking, ‘What am I doing here?’”

Philippa Whitford

Then: Consultant breast surgeon.

Now: MP for Central Ayrshire.

And… ‘I sit here and think: I used to do a useful job,’ says Whitford.

Photograph: Katherine Anne Rose for the Observer New Review

You used to have a proper job, I point out, because she’s now the new MP for Central Ayrshire but she used to be a consultant breast surgeon at the top of her field. “I know. That’s why it’s so awful, PMQs. I sit there and think: ‘I used to do a useful job.’”

One thing the new SNP MPs have done has been to shine a light on some of the more arcane practices at Westminster. Joanna Cherry, the new MP for Edinburgh South West, who’s another impressive woman at the top of her game – she’s a QC – said: “Some people have said they’ve found more about what goes on in the House of Commons as a result of the SNP tweets than they’d ever known before.”

It raises the question of why other parties haven’t challenged some of the more antiquated procedures. One of the most powerful and political acts the SNP has undertaken so far has been to simply show up. So many MPs simply don’t bother. “That’s one thing I have been impressed by,” John Crace, the Guardian’s parliamentary sketch writer tells me. “Their attendance levels. They turn up. They are definitely here to make an impact and to be noticed.”

They have been: there was a whole flurry of stories when they arrived and started “Defying convention!” as the Daily Mail put it. “The Scots have arrived!” ran the headline. “SNP MPs break the rules in their first week by taking selfies in the Commons as they celebrate election takeover with chips on the terrace.” It was illustrated with a photo of Mhairi Black, the new member for Paisley and Renfrewshire South, eating her lunch – chips and a slice – a photo taken by a fellow MP and tweeted with the caption: “Ye can take the lassie out of…”

Torcuil Crichton, political editor of the Daily Record in Glasgow, says that there was a certain amount of trepidation before they turned up: “The Conservatives had very successfully managed to demonise them. They had played a dangerous game, inflaming a fear of Scotland, causing both Lib Dem and Labour voters to turn to the Tories. And when they appeared in Westminster, I mean it was as if Westminster was waiting for aliens to arrive.”

Everything they did became a story. “The Scots are invading… the Labour benches!” ran the Mail’s next headline. “New SNP MPs defy convention to sit directly behind the opposition front row.” Among them, it stated “was the SNP’s 20-year-old Mhairi Black… asked about her choice of seat, she said: ‘I didn’t see any signs.’”

“She literally just walked in, chatting with Diane Abbott and sat down next to her – she didn’t know,” one SNP MP recalls. “It was like the story about us trying to steal Dennis Skinner’s seat – even he’s said that was complete rubbish.”

And then there was “clapgate”, when – instead of saying “hear hear” at something they agreed with, as if they were 18th-century landowners – they broke into that newfangled concept: applause. Or as the Mail put it: “Show some respect! Furious Speaker Bercow rebukes new Scots Nats MPs for breaking strict Commons protocol by clapping during the Queen’s Speech debate.”

They’ve stopped doing it now, sadly. “I think it was a real missed opportunity,” says Crichton. “In the Scottish parliament there’s applause all the time – it’s like an Italian opera. But the speaker censured them when they first did it, and then there was a pause. In that moment they should have carried on and overturned a centuries-old convention like that, but instead they swallowed it. And that was that. Now they shout ‘hear hear’ like everyone else.”

Mhairi Black

Then: Politics student.

Now: MP for Paisley and Renfrewshire South.

And… At just 20, she is the youngest MP since 1832.

Photograph: Katherine Anne Rose for the Observer New Review

I’ve read a lot about Mhairi Black before I meet her. While it seems gobsmacking to me that Stuart Donaldson is an MP at 23, Black was just 20 when she unseated one of Labour’s big beasts, Douglas Alexander, in what was one of the most astonishing upsets of the election. And she’s been the centre of much of the press – good and bad – since then. “It’s been mental, completely mental,” she says when I meet her in the central lobby, an ornate high gothic affair. “There’s just been so much… nonsense.”

We’ve barely reached the outside Terrace cafe overlooking the Thames and sat down when a woman with a bunch of teenagers comes up and asks if she can introduce her son and his friends. “Do you mind? I’ve just told them how you’re an MP and they couldn’t believe how young you are.” She poses for selfies with them, the teenagers looking rather overwhelmingly impressed. But then, I’m more than twice their age and I’m rather overwhelmingly impressed.

She’s the youngest MP since 1832, and she ran her campaign while studying for her finals – a politics degree at Glasgow university – and revised for her last exam in the House of Commons library. What was it on? “Scottish politics. Which was pretty funny. There was a question on the SNP though, so that was quite good.”

Last week, she found out she’d got a first. It’s impressive by anyone’s standards, though having met her, I’m not surprised. When I ask which she’s proudest of, getting a first or being elected to parliament, she says: “It’s humbling to have been chosen to represent people. There’s no bigger honour than that. But for me, personally, I’m most proud of getting my degree. I didn’t expect to get it at all. I just worked really, really hard.”

It’s a textbook answer, which from anyone else might sound phoney, but when she says it in her broad west coast accent – she sounds like a Glaswegian docker, basically – she does it with an authenticity that I actually believe. She’s not just impressive because she’s 20. She’s impressive because she carries conviction. When she talks about the poverty and deprivation in her constituency and the biting effects of austerity, she says it with authority.

“What I can’t work out about this place,” she says, “is whether they’re genuinely oblivious to what their policies are doing, whether they’re so out of touch that they honestly don’t see how much damage it’s doing, or whether they just don’t care.”

It was Black’s victory that brought home what a total bloodbath Scotland was for Labour. Douglas Alexander wasn’t just the shadow foreign secretary, he was the mastermind of Miliband’s campaign. What a shock it must have been for him, I say. “I imagine so, aye. He had his eyes set on being foreign secretary, trips to Washington and all that. And then along comes me. There was panic at the end. It was almost as if the national campaign was abandoned. I’ve lived in Paisley all my life, and I saw more of Douglas Alexander in the last month than I have in the last 10 years.”

Nobody expected her to win. And she’d never dreamed of standing until people kept telling her she ought to. “I took the same approach as everybody else, going, ‘Oh, come on. I’m 20. Don’t be daft.’ What convinced me in the end was that somebody said: ‘Who came up with the idea that parliament had to be middle-aged, middle-class guys anyway?’ That’s actually what the problem is. Parliament has to reflect everybody, because the more diverse opinions you get, the better quality the policy is.”

Exactly. Though being that person has its responsibilities. “I will still go to the pub and have a drink with my friends,” she says, explaining what her life is like now. “But you know. You can’t get moroculous.”

Moroculous?

“You know like being sick against a wall or something.”

Chris Law

Then: Leader of motorcycle expeditions to the Himalayas.

Now: MP for Dundee West.

And… He is that rare species, an MP with a ponytail. It has its own Twitter profile.

Photograph: Katherine Anne Rose for the Observer New Review

It feels genuinely exciting to have the likes of Mhairi Black in parliament because the young have been, and still are being, systematically turned over by successive generations of politicians. The reasons are well rehearsed – tax breaks for the old because they’re the ones who vote whereas the young don’t – but then, of all the things that the Scottish referendum did, energising young people to take an interest in politics is perhaps one of the most significant.

“They were just so engaged,” says Stuart Donaldson. “During the referendum there was this massive event in the Glasgow Hydro and it was full of schoolkids asking questions to people from both sides of the campaign. To see that was really amazing.”

There are other things that perhaps the rest of British politics could learn from the Scottish example. Not least the fact that what’s most striking about the SNP MPs I meet is how normal they seem. Only one talks to me as if she thinks she’s on Newsnight. The rest are disarmingly like actual people. “It was striking when they first arrived,” Torcuil Crichton tells me. “They were posing on the steps of St Stephen’s for photos, and I just listened to them chatting and thought, ‘Wow.’ It really is a cross-section of people and accents. Some of them have only been members of the SNP for six months and some of them are lifelong nationalists but they’re from all corners of Scotland and they’re all interesting, fully rounded people.”

With some unlikely stories. There’s Deidre Brock, who was born and grew up in Australia and in her previous life, as an actor in Sydney, appeared in Home and Away. There’s Chris Law, who someone recommends I talk to on the grounds that “he has an interesting background and he doesn’t look like an MP”, which turns out to mean that he has a ponytail and worked for a long time in north-west India, leading motorcycle tours of the Himalayas on vintage Enfields. There’s John Nicolson, who’s a familiar face from the television as a BBC journalist. And Tasmina Ahmed-Sheikh, who has become the SNP’s first Muslim MP and has a past that includes being a member of the Conservative party and a Bollywood actor.

A noticeable number of those I interview are gay – Joanna Cherry, Mhairi Black, John Nicolson. The SNP not only has a higher percentage of gay MPs than any other parliamentary party in Europe, but, according to John Nicolson, “because of our presence, it’s the most gay parliament in the world”. And it’s striking when they tell me about their commutes, by planes, trains and automobiles – Ian Blackford, an ex-banker from Skye, explains how he leaves “at 6pm on Thursday and I get home between 2-5am on Friday morning” – because they do actually live in their constituencies.

John Nicolson

Then: BBC TV journalist.

Now: MP for East Dunbartonshire.

And… Nicolson compared the House of Commons to Hogwarts.

Photograph: Katherine Anne Rose for the Observer New Review

The people they represent are their friends and neighbours, whereas nobody is even trying to pretend that Ed Miliband is hanging out with his mates in Doncaster in his leisure time. And the bloodless career politicians who have bounced from PPE at Oxford to a thinktank to the front bench or shadow front bench are nowhere to be seen in the SNP. Not least because no one in their right mind thought there was any career in Westminster politics for an SNP MP.

The difference between their energy, optimism and conviction and what I saw at the Labour party conference in Manchester last autumn is striking. I went there to do a story for the Observer New Review and wrote about how it had all the passion and authenticity of a L’Oréal sales conference, with various PPE graduates from Oxbridge arguing about the product lines. And I always like to tell the story of the MP I knew – a PPE-er from Oxford – who went on to become a minister after bagging a safe seat in a northern constituency he had no connection to whatsoever. He was invited around to Sunday dinner by one of the leading lights in the constituency. “So I turned up at 8pm with a bottle of wine, and he was like, ‘Nay lad, I said dinner. We had it hours ago.’” In fairness, he told that story against himself, but, well, it’s not really one of the great, inspirational tales of the Labour movement that they’ll be telling 100 years from now.

But, then, it’s a question at the moment if there even will be a Labour movement 100 years from now. “Labour just look so crushed,” says John Crace. “It’s hard to find a Labour MP with a smile on his or her face. The SNP are looking and sounding more like a proper opposition because Labour is in a total mess.”

When Chris Grayling announced his surprise English votes for English laws (Evel) bill last week, most of the Labour front bench were nowhere to be seen – there was a leadership hustings event going on at the same time. (The SNP MPs are predictably outraged at the proposals but there are a few questions to answer: it’s only after chatting to Philippa Whitford, the breast surgeon, at length about her role as the party’s health spokesman that she points out that health is actually a devolved issue.)

Looking like a credible and organised opposition is “their game”, another political editor points out: “It’s theatre. They’re putting on this performance but their interest, really, is in screwing the system.”

Roger Mullin

Then: Teaching applied decision theory at the University of Stirling.

Now: MP for Kirkcaldy and Cowdenbeath, Gordon Brown’s former seat.

And… I was the first person to break the television swingometer,” he says.

Photograph: Katherine Anne Rose for the Observer New Review

And I have various depressing chats with people on the future of the Labour party. “Without the Scottish Labour MPs, it’s going to be extremely difficult for Labour to recover without winning large chunks of the south-east, and it is hard to see how they’ll do that,” says Helm. “With Labour demoralised and the Lib Dems almost wiped out and invisible, the SNP has become the most interesting, dynamic force in British politics, and certainly in opposition politics at Westminster. They have a really clear vision, a dynamic, good, young female leader, and they just pulled off a phenomenal thing.”

It’s a jovial MP called Roger Mullin who really conveys the depth and despair of the Labour mission in Scotland. I’ve just interviewed Deidre Brock, and she sends him over to find me on the terrace. He sits down with a pint in his hand. He’s an SNP lifer who, at the age of 67, really didn’t see this coming. In his maiden speech he pointed out that he’d first stood for parliament in 1974. “I said, ‘It’s been a rather long campaign.’” And then tells me how he’s “the new Gordon Brown”.

He’s the new MP for Kirkcaldy and Cowdenbeath where, in 2010, Gordon Brown won a 23,000 majority. In 2015 Mullin converted that into a 10,000 majority for the SNP. “I was the first person to break the television swingometer,” he says. He’s entirely gleeful when he tells this story, as he deserves to be, but it brings it home to me because, whatever else Gordon Brown was, he was a true believer: in Labour, in Scotland. His intervention in the referendum is credited with helping to save the union, but the sight of the party standing side by side with the Conservatives was too much for most Labour voters to swallow.

“It wasn’t entirely Labour’s fault,” says Crichton. “What happened in Scotland is not unique. There’s a massive wave of anti-politics that’s sweeping the world. It’s a global phenomenon, as is a surge in nationalism. Labour had a bad leader and took the Labour vote in Scotland for granted. But it fought for the union and it paid a high price.” The road to Downing Street, he points out, now “runs through Glasgow”.

Tasmina Ahmed-Sheikh

Then: Tory and actor.

Now: SNP MP for Ochil and South Perthshire.

And… She once starred in Bollywood films.

Photograph: Katherine Anne Rose for the Observer New Review

And as impressive as many of the SNP MPs I meet are, their endgame is another referendum and independence, and if that happens the Conservatives may well become the party that rules for 1,000 years with David Cameron as the new Kim Jong-il and the rest of us destined to live in a country in which George Osborne makes more emergency interventions to ensure that even dead, rich people aren’t parted from their money. It’s why the Tories are being so nice to them, says Crichton. “They’ve got a hug-a-nationalist policy because they know the SNP divides the left.”

I’m not entirely sure either how the SNP has managed to convince Labour voters that it’s a party of the left, when many of its MPs aren’t. I try to get Tasmina Ahmed-Sheikh to tell me her road to Damascus moment when she realised she wasn’t a Conservative any longer, and all I’ll say is that she might want to work on that answer. And its track record in the Scottish parliament isn’t exactly impressive, says Crichton. “They’ve only introduced one policy since 2007 that has redistributed wealth.”

Late at night in the terrace bar, I meet a very drunken Scot, a guest of an SNP MP, who nonetheless describes them as the “barmy army”. He points across the table at Michelle Thomson, the new member for Edinburgh West. “This one’s a right firebrand. As well as a property developer, of course. She’s like the rest of the party – a complete mess of irreconcilable contradictions.”

“I’m sorry,” says Thomson. “But I don’t even know who you are?”

At the moment the SNP MPs present a united front but that can’t last for ever, and nor can their current levels of popularity. I do start to understand, though, how MPs get so comfortable here. The terrace bar, with Big Ben bonging into the night, has the best view in London: to the left, the soaring faux-gothic buttresses of the Palace of Westminster, to the right the London Eye, straight ahead a scene of double-decker buses crossing Westminster bridge. It’s like the opening scene of a Hollywood film set in London. And all around, arresting sights such as Michael Gove drinking subsidised white wine and large groups of men (Tories? Maybe not…) getting in the champagne.

Kirsten Oswald

Then: HR professional.

Now: MP for East Renfrewshire.

And… She unseated Scottish Labour leader Jim Murphy.

Photograph: Katherine Anne Rose for the Observer New Review

It’s the best workplace ever. There’s a ton of bars and restaurants where MPs hang out at all times of the working day – the sun isn’t even past the yardarm when I see Gove hitting the Sancerre. The SNP MPs have colonised the Sports and Social Club, which is where a lot of the parliamentary staff go, and which has a karaoke night. And there are always colleagues around to gossip with. People keep having conversations about “the Tories’ evil plan”, which I only belatedly realise is actually their Evel plan.

It’s only been a couple of months, but John Crace tells me he already thinks they’ve become institutionalised. “They’re much more observant of parliamentary procedure. They’ve stopped taking photos of themselves. The Mail and Telegraph were portraying them as ignorant and unworthy so perhaps they’re trying to show they are serious. But this place does get to you. It feeds on your self-importance. You suddenly have a budget for staff, and you’re flying home on a Thursday night. I’m sure it must be happening to them because it happens to everyone. I’ve been here a year, and it’s probably happening to me. That’s the nature of power in Westminster.”

It’s not in the SNP’s interests to get comfortable here. But it’s certainly an insight into what seduces so many politicians. Why they start talking like politicians. Why they don’t ever want to leave. It’s on the same terrace that John Nicolson, the ex-BBC journalist, gives me a list of phrases he’s sworn to never utter. “I’m never, ever going to say, ‘frankly’,” he says. Can you not talk about hardworkingfamilies, please, I say.

“I’m never going to talk about hard-working families. And I will not say ‘fit for purpose’.”

We’ll see. Ed Vaizey pops over while I’m talking to Nicolson to congratulate him on a question he asked in the BBC debate, and it all feels a bit cosy. As Tommy Sheppard points out to me: “It operates like an exclusive club.” Given that Sheppard actually ran a club, it’s possible he knows what he’s talking about. “All those doormen who greet you by name. And why are we called ‘members’ anyway?”

It’s been a brilliant rebranding exercise, the new-look SNP. They repackaged nationalism as social justice, and delivered a message of optimism and hope that the electorate bought. And they’re there, in the House of Commons, turning up, being smart and sensible… and ultimately conspiring to leave the rest of us stranded, for all eternity, shrugging in listless apathy at what passes in this country for political debate.