John Oliver interprets Britain's quaint ways for the US audience of the Daily Show. He explains how he gave host Jon Stewart a 'schadenfreudegasm' when the pair discussed a certain newspaper scandal

John Oliver, the British comedian whose job it is to explain the eccentricities of our nation on America's The Daily Show with Jon Stewart, has a characteristically unpretentious description for the process of writing jokes about the news. It is, he explains cheerfully, "like working in a sausage factory, trying to make a palatable sausage from some of the worst ingredients you can imagine – you've got all this disgusting stuff and then you just try and find something you can swallow".

The huge swathe of Americans who regard the show as essential viewing, might protest at such an undignified metaphor. The late night satirical show, which has been running since 1996, has made a hero of its host to liberal-minded viewers both sides of the Atlantic and it's become fashionable to opine that the show, which has 14 Emmys to its name, is now more powerful than the straight news shows it lampoons. Stewart plays a fake anchor, tirelessly skewering the absurdities of US politics while Oliver plays his fake Senior British Correspondent, a walking compendium of British cliches. Oliver, who is one of the show's writers (one of those Emmys is his) is seriously downplaying it when he says, "if there are news stories going on, people might then want to tune in to see what we do with it".

Lately, that sausage metaphor has seemed particularly apt: the "ingredients" don't get much more unpalatable than the revelations surrounding the News of the World phone-hacking scandal. The clip of him explaining just how deep the scandal goes has become an online hit, not least the moment when he tells Stewart, affecting gloom over US failings as a country, that he's about to give him a "schadenfreudegasm" of national, institutional shame.

Inside the show's Manhattan studios, a wall is almost taken up by a huge image of Oliver's face and while his own show on Comedy Central (which goes by the no-nonsense title of John Oliver's New York Stand-Up Show) has made that face even more recognisable, Oliver still retains the demeanour of the class nerd trespassing at a cool kid's party.

I meet him after the Daily Show's evening filming when, already researching tomorrow's show to be ready for its first meeting at 9am, he welcomes me into his small and demonstrably tidy office with the words "Sorry… it's a bit messy."

Oliver joined the show in 2006 – earnest, bespectacled and with thick eyebrows usually hitched into startled mode, he instantly proved the perfect foil to Jon Stewart's suave authority. His first appearance, a segment on immigration, included a cod-Dickensian tale of his journey from the orphanage ("yes Jon, all British people grow up in orphanages") to the land of the free.

"It was the most generic series of cliches about what a British person's past would be like: they flew everywhere by umbrella, they're an orphan, they subsisted by pickpocketing, they lived on the street, they were a chimney sweep. That is the basic process for any British child: making your way through the Victorian streets of London, flying everywhere, breaking into song when you can."

His status as the show's lone Brit is lampooned off screen, too.

"There's a lot of history between the two nations to stick to each other. If you work on a comedy show, your basic form of communication is teasing. That's generally how we speak to each other: you communicate the information between the lines of insulting sentences."

Over the last few weeks, that's meant filling in his colleagues on British tabloid journalism and explaining why revelations such as the News of the World hacking British soldiers' phones, "perhaps aren't that surprising".

But has he felt any of his own Brit shame over the scandal? "I feel non-stop Brit shame!" he exclaims. "I'm in a country we conquered, I'm made to feel shame all the time! It's a grimy story so in explaining just how grimy it is to people here, you've got to say 'yeah, we've got a problem'. But it's always fun to have a big, serious thing to find an angle on and make comedy from."

For years, as a writer on the show, that was the failures and ineptitude of the Bush administration, but it wasn't always subject matter that Oliver relished. "There were times, especially towards the end, when the things that were coming out were so bad, so depressing," he says.

He cites the scandal of the Walter Reed Medical Centre – the hospital where wounded soldiers allegedly suffered neglect and unsatisfactory conditions. There was a nationwide outcry after the Washington Post reported on it in 2007.

"It's not much fun to be angry all day and you want to provide some kind of catharsis with comedy so you try to process your feelings into something that's funny."

But it's not just funny: famously, a sizeable slice of America's population claim to get their news from the show. If you're aged 18 to 34, you're more likely to watch the show than network news. Oliver gets very animated about this. "It can't be true!" he exclaims. "If people say they get their news from us then it's an indictment of news shows rather than a compliment on our journalistic skills, of which we have very few."

That, I think, is an instance of Oliver's good old British self-deprecation: the show is unfailingly astute and informed (in 2008 The Project for Excellence in Journalism released a report suggesting that The Daily Show comes close to providing the complete daily news.) It's also respected enough to have attracted a roll call of current and former national leaders as guests. Tony Blair and Barack Obama have both sat opposite Stewart. Last week, Stewart sipped Powerade with Pakistan's former president Pervez Musharraf before quizzing him about whether the country had harboured Osama bin Laden. It may be comedy, but it takes itself very seriously.

"When you're dealing with serious subjects, there is a pressure to be absolutely sure that you know what you're doing," Oliver says. "You're playing with much bigger toys then so your joke has to be extra good. You have to acknowledge the responsibility – that if you're going to go into a serious area you're not going to do it glibly."

That necessitates a near-addiction to the news.

"I was interested in politics before but you end up mainlining it like heroin here. For the first three years, I had CNN on all night when I slept. Terrible idea."

He shakes his head and frowns. "I had these weird dreams. Terrible. Not remotely healthy. So now I don't do that anymore."

Oliver, now 34, was born in Birmingham and five years in New York haven't dinted his Brummie burr. ("I am determined not to speak like these savages!" he says of his compatriots.)

He describes himself as an "awkward" teenager. "I would hate to meet myself at 15. That should be the case – if you don't find yourself saying that, you're a profound arsehole."

After having abandoned his boyhood delusions of professional footballing, Oliver went to Cambridge where he neglected his English degree to write and perform in the Footlights comedy troupe with his friend Richard Ayoade.

"I wasn't really engaged in the academic side of it," he says, happily admitting that he learned to bullshit rather well. "But for comedy it was incredible because you get a chance to fail relentlessly, in a very safe environment. And that is a privilege that's impossible to overstate."

His stand-up career flourished and Oliver began meeting some of his comedy heroes. When he made Armando Iannucci laugh (Oliver worked on his 2003 topical review show Gash), he told himself, "if that's all I get to do, if it doesn't work out then that's fine, that's more than enough. I thought everything from this point is beyond what I could reasonably expect."

That included this job, of course. Oliver was a huge Jon Stewart fan before the show headhunted him.

"You're always going to have that imposter syndrome – there's going to be a point where whatever clerical error was committed is going to be discovered. That first day I remember I didn't really have time to be as terrified as I should have been. It happened so quickly that it was a blur. A helpful blur."

He left the UK in such a hurry that his stuff is still in storage.

"Psychologically, not that I particularly delve into my psychological stuff, I'm sure that leaving a room full of possessions in London goes back to that sense of 'when this detonates, when this all fucks up', it will all be there to go back to."

Those fears have finally begun to ease though.

"I feel more at home knowing I'm not really at home. It takes all the pressure off you trying to fit in! It's been great – when you're not supposed to fit in you tend to just relax. But as you mentally start making a place your home you realise it's not your call to make – it's in the hands of an angry-looking person in a booth at the US embassy."

Now he has a green card, but for years he lived in terror of the border control officials.

"The last time I was so nervous and I got this really furious-looking woman. She looked up and she said, 'give me one good reason why I should let you back into this country to make fun of my president.' And my heart fell through my stomach. And then she said, 'oh, I'm just kidding, I love the show.' I think she was expecting me to laugh and I was so crushed and terrified by feeling my life pulled out from underneath me that I don't think I responded in the right way."

Making fun of the president has in fact been "the most interesting thing to get your head round". When Obama was elected, Oliver was personally and professionally delighted.

"Comedically, I thought great, this is going to be a whole different kind of joke to tell. You get to reset, you're not writing just from outright, relentless despair, now it becomes more complicated than just cathartic primal screams."

He filmed a segment at the inauguration where he had the strange experience of witnessing "a genuine moment of history with the sole purpose of in a way trying to undermine it. I looked back on that the other day because I couldn't remember what we'd done and there's one moment I guess is pretty good.

"Literally, as he swears into office I'm kind of jumping up and down screaming going, is this incredible? Yes! Is everyone sowing inevitable seeds of disappointment? Yes! Do we care? No!"

He grins. "I guess that played out. It helps to lower your expectations. That's a very British view of the world isn't it? 'Just lower your expectations.' Here it's 'the sky's the limit' and in Britain it's like whoa, don't worry about the sky, just try and get through the day."

And he happens to be doing all right on that count. He grins again. "Generally, I end the day laughing, and if I don't I'm double-fucked because I'm miserable and I haven't done my job."

• This article was amended on 26 July 2011 to correct the year of The Daily Show's first transmission to 1996.