Jeremy Corbyn and John McDonnell

"You can't change the world through the parliamentary system," said John McDonnell, as he settled down to talk with his friend, and fellow Labour MP, Jeremy Corbyn, in Parliament's Committee Room 14. This isn't what you'd expect to hear from a politician so close to election time, but then again, these two aren't quite your normal MPs.

It was long gone 9PM by the time we got chatting, both blokes having been keen to speak to attendees at the meeting that had just finished, until an aide had finally told them to head off. They'd been hosting the final night in a series of events called the " People's Parliament", which over the last 12 months opened the doors of Westminster to various left-wingers, holding meetings on issues like sex work, police corruption and the evils of capitalism.

"Getting political representation is important, but change comes through using direct action, campaigning, and trade unions", McDonnell continued, both clearly comfortable letting the other take the lead.

Jeremy Corbyn, 65, has been the MP for Islington North since 1983, while McDonnell, 63, has held the seat in Hayes and Harlington, West London, from 1997. In the final five years of the last Labour government (2005-2010), they defied the party whip a quarter of the time, making them the most likely of all MPs in the House of Commons to rebel against their party line. The right of British politics and the mainstream of the Labour Party would see them as throwbacks – ageing socialist dinosaurs reminiscent of a by-gone era when Tony Benn would snipe at Margaret Thatcher over the dispatch box. Meanwhile Labour's socialist true believers would probably say the very same, but as a compliment.

Corbyn spends his time with the Palestine Solidarity Campaign, Stop the War Coalition, and rocking up to picket lines in support of struggling workers. McDonnell has played the maverick too. During a speech to the GMB Union in 2010, announcing he wished he could go "back to the 1980's and assassinate Thatcher", remarks he now labels as "sickening" and "distasteful". He was suspended from the House of Commons for five days back in 2009, after grabbing the Speaker's mace in protest of the then Labour government's decision to allow a third runway at Heathrow. Both are members of the Socialist Campaign Group, the small lefty sect of the Parliamentary Labour Party.

While the pair have spent years shouting from the back benches, the likelihood of a government with the slimmest of majorities taking power after the election could give them significant bargaining power. Earlier in the evening, I'd been handed a copy of "The Left Platform", a policy document that the left of the party are pushing as they head into the election. The headlines are radical – on tackling the deficit, an end to austerity, calls for a wealth tax, a minimum wage of £10 an hour and the nationalisation of public services.

According to McDonnell, this has the backing of a bloc of "30 to 40 MP's." The demands are there to set the debate, he explained, "but it will ultimately come down to what people are willing to vote for." Could this be a threat to Mliliband?

"I think what we're trying to say to the Labour front bench is, 'don't ignore the left – we're here'. When it comes down to certain issues, if this a Government thinking it's going to implement austerity, with our support, they've got another thing coming," said McDonnell.

McDonnell is hopeful of a small Labour majority, and with the numbers they say are on board, they could fuck things up for a Miliband government that pursued austerity – refusing to vote for their policies, effectively meaning Miliband wouldn't have a majority. That could potentially bring down their leader – it's quite a threat.

"It's not a threat", according to McDonnell, "it's a statement of fact."

"What we are saying to the leadership is that we won't be voting for austerity, and when the day comes there'll be enough Labour MP's, with enough support out there, to stop them."

The opportunity to have a real impact arguably vindicates their continued membership of a party that they have been politically at odds with since its "modernisation" and move to the right under Blair 1990s. Today's young radicals are relatively unlikely to join the Labour Party. I asked if they'd be in a hurry to join Labour themselves if they were new to left-wing politics.

"I think you can see why not, people are pissed off at the Labour Party, especially young people," said McDonnell.

Corbyn too didn't rush to sign me up, "Get involved in campaigns, in a union, with peace movement, get involved with Occupy & UK Uncut", he said, before adding, finally, "and also be in a political party."

So where did it all go wrong for Labour, from a left-wing point of view?

Corbyn reckons it's the fault of those who see the party as a purely parliamentary force, rather than one wing of a broader social movement. "The original structure was of trades and labour councils, our intrinsic trade union link on a local level. It's been under attack as long as I've been in, but it's still there."

That attack has intensified in recent months. In 2014 Miliband pushed through policy to reduce the power on union's in the party, just last month being accused of an " old fashioned stitch up" by Unite, the country's biggest union, in a row over candidate selection.

"The worst period was in 1993. People were so desperate to win after losing a series of elections; they allowed Peter Mandelson to turn the party, or at least some of the party, into New Labour. We never signed up to it, neither did most of our members," insisted Corbyn.

But it happened. The left of the Labour Party was calling the shots less than it had ever been and Blair, Brown and Mandelson took the helm. Under their leadership, the Labour Party were in Government for 12 years, in which time they refused to reverse the Thatcherite curbs on trade union powers, came up with tuition fees, and introduced substantial privatising reforms in education and health – all anathema to my interviewees.

McDonnell's eyes thinned, clearly still pissed off. "We had a coup, by a group of three extremely well funded neoliberals, taking over and party isolating the left as much as they could, driving through policies on behalf of capital."

This was back in 1994, over 20 years ago, and yet Corbyn too remembered it with venom. "When John Smith [former Labour leader] died, it was less than six hours later that word was going round that Blair was going to be standing for leader. John's body hadn't even left the hospital."

Unsurprisingly, Blair remains one of those still keen to sever the ties with the unions, last month reportedly securing £1 million worth of funding in an attempt to push away from union links. Corbyn wasn't impressed. "Blair should silence himself, and go and play with his money somewhere far away... I've always thought he should face the International Criminal Court for his actions over Iraq."

A common criticism of the likes of McDonnell and Corbyn is that they're a distraction to make a sold out party look legit – wheeled out at protests and leftist meetings to provide Labour's disillusioned socialist members with a glimmer of hope and stops them forming some Syriza style break-away. Maybe it'll get better, we've got Jeremy !

"That's very unkind," replied Corbyn, "I willingly attend demonstrations because I believe in it. I do not believe I'm being wheeled out for anybody thank you very much."

McDonnell was more reflective. "I hear your point, but it's this point we've been arguing – it's our party, not theirs. We're not the interlopers. We stand in the centre ground of the Labour party and our traditions. The policies we are advocating go right back to the beginning."

But would they leave, if the party continued to stray from their socialist ideals?

"That's what they want", they both told me. "It would be so much easier for the right, for Blair and others, if we either left voluntarily or they could expel us," said McDonnell.

The question seems more relevant than ever as Britain's two-party system opens up to parties which seem, to varying degrees, to be to the left of Labour – the Greens, the SNP and Plaid Cymru. In fact, flicking through these two's vision for Labour reminded me of another document – the Green Party's manifesto.

"Well, the Green Party manifesto reads like what we've been doing for the last 17 years in here", retorted McDonnell. "If the Greens have socialists within the party that agree with us, then that's excellent."

It's a well-rehearsed response, but I wasn't left convinced. You're telling people to vote for your party, which doesn't have policies you would back, instead of a party – the Greens – that do?

"It's having to come to terms with the electoral system, and where we can make those advances", I was told by Corbyn, who looked over to McDonnell, nodding. "The Green Party might subscribe to some of the policies that we are advocating, but it's not a class based socialist party."

I press them more. The Labour Party is throwing a tonne of resources at getting the Green Party's only MP, Caroline Lucas, out of her Brighton Pavillion seat. Does that not piss them off? All this effort on trying to topple a natural ally, instead of focussing on seats that UKIP or the Tories are hoping to take?

"I'm focussing any resources on South Thanet, defeating Farage," replied Corbyn, not for the first time actively avoiding a question.

I asked again. There was an uncomfortable silence.

"She is in one party, we're in another party. I think we should talk about something else, thanks."

Fair enough – back to their own leader. I asked them for a simple yes or no. Is Ed Miliband the right person to be leading the party into the election?

Corbyn sighed, "he is the leader, it's not going to change. Frankly it's not a terribly relevant question" – about the least ringing endorsement I've ever heard.

McDonnell chimed in, "let's be clear, we don't believe in leaders."

I thought that was a weird thing to say for someone who ran to be Labour leader twice. Back in 2007 he failed to get enough support, and did the same again in 2010. Corbyn was considering running as his deputy. Sour grapes?

McDonnell faltered, slightly, for the first time. "We believe that leaders should be following the masses. We only ran in leadership campaigns to get our ideas across, to use it as a platform."

"One of the first things we'd have done, had we won, was transform the idea of leadership within the Labour Party."

As election day nears and a party winning a strong majority unlikely, it seems that McDonnell, Corbyn and apparently tens of Labour left-wing MPs may have the chance to challenge their leaders once more. Shouting from the back-benches and voting against your own party takes on a renewed significance when that party has a wafer-thin majority. After the 7th of May, we may be hearing a lot more from the likes of McDonnell and Corbyn.