Ian Hislop bustles. There's no other word for it. He exudes urgency and purpose. One minute the reception at Private Eye's chaotic Soho office is quiet, and a matronly receptionist is making me a cup of coffee. The next Hislop has arrived, and the atmosphere is transformed. He has presence, even at a generous 5ft 6in and with that schoolboyish tendency to scrunch up his face when he laughs.

Dressed in a blue suit, with a pair of sunglasses poking out of his top pocket, he looks like the successful entrepreneur he is. Hislop runs the satirical magazine Private Eye, natural home of anarchists and dropouts, while looking like the head of the local Rotary club.

Hislop celebrates 25 years as editor this year – he took over from Richard Ingrams at just 26. He is keen to downplay that anniversary, but is certainly not downplaying the fact that his magazine is about to mark its 50th birthday. A celebratory book by Private Eye staffer Adam Macqueen is being published, and the Victoria and Albert Museum is staging an exhibition showcasing the magazine's covers and cartoons. It is all dangerously respectable, though, as Hislop says, critics have been complaining since 1962 that Private Eye has become part of the establishment.

The first thing you see as you come through the front door are photographs of the men – they are all men – who kept the magazine afloat in its early years. "We call this the wall of death," Hislop says. Most of those photographed have, indeed, passed on, at dismally young ages – Peter Cook, Auberon Waugh, Paul Foot, John Wells, Willie Rushton. "Bons viveurs tend not to live to a very great age," Hislop says of Waugh. The ultimate bon viveur – in the couple-of-bottles-of-vodka-a-day sense – was Private Eye's proprietor, Peter Cook, who died at 57 but at his death looked a bloated 77.

Private Eye remains something of a boys' club. Hislop says he employs two women journalists, but admits there aren't many women making jokes on the magazine. For this he blames the women, not the Eye. "Women either don't put themselves forward or they're not part of gangs of blokes showing off at school and university who then turn that into a living or a way of communicating. Maybe women don't have to do that."

Fifty years on, men from public schools remain the heart of the joke factory, and Hislop fits squarely into the mould. His father was a civil engineer who travelled widely for work, and Hislop had a peripatetic childhood, spent in Nigeria, Kuwait, Saudi Arabia and Hong Kong. He boarded at Ardingly College, a public school in Sussex run on Christian principles, which provided a sort of surrogate family and where he was head boy. It is tempting to see him moving seamlessly from public school to another institution with strong codes, a keen respect for its past and a ready-made surrogate family – Private Eye.

Cartoonist Nick Newman, the son of an RAF officer, was a couple of years ahead of Hislop at Ardingly. "We first met in the school play," Newman remembers. "It was an awful sort of 'educational' production about the Peterloo massacre. There was much sniggering in rehearsals as all these posh public schoolboys tried to be working class. Later, we did a few revues, very sub-Python. I was 16 and he 14. At that age you don't really talk to anyone in the year below, but Ian could mix with anybody. He didn't have that shyness that other people have with their elders. When his dad died, I think he grew up very fast."

Hislop's father died at the age of 45, when Hislop was 12. "Because he died young, he was a very strong force," he says. "For a long time I thought I should be a civil engineer. That seemed to be the only thing worth doing, and I chose the wrong subjects at A-level. I read all the sciences to start with, and then had to admit, 'This isn't what I want to do' and changed course." He was close to his mother, who after her husband's death made her home near the school. "It was quite selfless of her really," he says. "I had a built-in life and community, rather than having to share in the grief. My mother was a terrific force in my life. Wartime-generation woman, hadn't gone to university but should have done. Was very funny, very verbal, very clever, very witty." He has an older sister, to whom he is also close.

Hislop studied English at Magdalen College, Oxford, where he collaborated with Newman on a satirical magazine called Passing Wind. "I'd been doing it with another friend, but he'd lost interest," says Newman, "so when Ian came up he took it over. He was more focused than I was." Hislop admits he is a workaholic, and attributes it – as with so much else – to his absent father. "He loved what he did, which was a very strong influence. For him work was an endless pleasure." His father was Scottish born and Hislop sees his own workaholism as a "Scottish genetic, Presbyterian link".

Hislop and Newman were by now joined at the satirical hip, and worked together on the influential 80s satire show Spitting Image. Hislop had also started writing for Private Eye, after impressing editor Richard Ingrams when he interviewed him for Passing Wind while still at Oxford. Ingrams was only in his 40s, but had already edited Private Eye for two decades and, according to Hislop, was exhausted after a succession of bruising legal battles. In Macqueen's book, the latter years of Ingrams' editorship are painted in bleak terms, with the tone of the magazine becoming bullying and elitist, and I ask Hislop whether his predecessor, who still attends the collective joke-writing sessions, will be hurt. "The last thing I would want to do is hurt Richard," Hislop says, "because he's an extraordinary figure in my life." Indeed, Hislop likens him to a "substitute father".

One difference between Ingrams and the improbably youthful figure he chose to succeed him concerned gossip. "I thought society gossip was outdated," Hislop says. "It was just leg-over constantly. I'm often accused of being prudish, but the opposite is true. I thought endlessly recounting that people's marriages had failed didn't seem that thrilling." The Hislop alternative? "I'd always thought the thing that defined the Eye at its best was investigative journalism and jokes, and I suppose what I've put in place of society gossip is professional gossip – people talking about how their industries, businesses, professions work, rather than saying the Duke of Cumberland was seen in White's with someone who wasn't the Duchess of Cumberland."

The principal purveyor of that old-style gossip on the Eye was Nigel Dempster, and he and fellow Daily Mail journalist Peter McKay staged an attempted coup against Hislop's succession in 1986. They took Cook, who owned most of the shares in the magazine, out to lunch, got him drunk (never difficult) and marched back to the office to confront Hislop. Instead of firing him, Cook said, "Welcome aboard." "If Richard had appointed Christine Keeler, I might have intervened," Cook said later, "but Ian was the ideal choice."

Hislop praises Cook for his support in those early battles and for his comic genius, but wonders whether he could in turn have helped save him from the bottle. "He did a brilliant last show with Clive Anderson, and I got a pang of guilt then because I thought what Clive had done is not indulge Peter. I thought, 'Had we indulged Peter because he was so naturally funny?' I had ended up working for and with one of my heroes, so it was quite difficult to say, 'You know, I don't think you should drink so much.'"

Unlike Cook and many of the first-generation Eye stalwarts, Hislop is no hell-raiser. "Every 10 years he gets a bit drunk in the evening and wakes up with his contact lenses in," says Francis Wheen, one of the first people Hislop signed up when he became editor and now his de facto deputy. "He lives a quiet life down in Kent." Hislop is married to novelist Victoria Hislop, whom he met at Oxford. Her success came in her mid-40s, when in 2005 The Island became a bestseller. "I'm now plus one," he says when I ask how her celebrity has affected their relationship. "I go to literary festivals and hang about while she talks." They live in Sissinghurst, and have two university-age children, Emily and William.

Although Hislop was a keen student performer, and took a revue show to Edinburgh with Imogen Stubbs, he is not, says Wheen, "a great one for showbusiness". He is good friends with John Sessions and Harry Enfield from their time working together on Spitting Image but, Wheen says, "he does like to keep parts of his life separate from others. At his 50th birthday last year, this coach turned up and someone said, 'I'd now like to make a speech on behalf of the Kent friends.' "

Wheen does not record any speeches by Hislop's enemies, though there are enough of them to fill several coaches. He has had a decade-long feud with Piers Morgan, prompted by Eye revelations over alleged insider trading as well as stories about Morgan's private life. Morgan was so furious, he sent a team of reporters from the Daily Mirror, which he then edited, to dig for dirt on Hislop.

"They managed to find out that I'd once got drunk at university," Hislop says. "He devoted amazing resources to putting people on my door, sending people down to the village, contacting people I'd been at school with." They even got in touch with the vicar of the Hislops' church to ask whether his congregant had confessed to anything distasteful, not realising he was an Anglican and didn't take confession. A complicating factor was that their sons were in the same class at a prep school in south London for a couple of years. "The two of them were having this huge fight and then having to bump into each other at parents' evenings," Newman recalls.

If you're editor of Private Eye, it may be imperative that you have a stainless private life. "I like to imagine that when he was about one year old, a search went out around the country – like the search for the Dalai Lama," Wheen says. "Where is this boy who is so pure and spotless that he can edit Private Eye and not be accused of hypocrisy? It's amusing to me that he and Rowan Williams seem to get on tremendously well, but I can see why. In his quiet way, he's a vicar manqué. He gets fanmail from bishops." Which is not to say that Hislop is a saint. "He can shout and go red in the face," Wheen says. A section of Macqueen's book is devoted to the editor's furious memos, handwritten on pink paper.

Hislop's most recent spat has been with Andrew Marr over the injunction Marr had taken out to block any discussion of an affair he had had. "There were lots of injunctions taken out by footballers," Hislop explains, "but the one that mattered was Marr's, because he had been asking Gordon Brown about his pharmaceutical usages and interviewing Blunkett about his baby." He labelled Marr's behaviour "stinking hypocrisy". "He knew he was wrong," Hislop says, "and he admitted it in the end."

The pursuit of Marr added to the perception of Hislop as a moralist. Macqueen plays up that view, and finds the tenor of his Eye different from that of Ingrams. Hislop is sceptical. "It would be difficult to be more overtly moral than Richard. He has very strong views about morality, and was very insistent on them in terms of marriage and homosexuality in a way that I don't think I am. People say I'm judgmental, but all journalism is judgmental. Vice, folly and humbug – it is the point of satire really. Marr is a very good journalist, and he should know better."

What about Angus Deayton, the presenter of Have I Got News For You, who was sacked in 2002 after tabloid revelations about his private life? Deayton blamed Hislop and Merton for ousting him. Wasn't that unduly moralistic, given most viewers of the programme wanted Deayton to stay? "The moment for me was when Christine Hamilton came on the programme," Hislop recalls. "Angus introduced her as, 'The wife of the disgraced Neil Hamilton' and she said, 'If he's disgraced, what are you?' At that moment I thought, 'Your role is unsustainable here.' I said, 'You may not need the entire moral high ground, but you need a couple of inches' and he didn't have it any more. I felt either the show went or he went."

A recent column by Martin Kettle in the Guardian described Hislop as "the single most influential voice in British politics". But Kettle did not intend it as a compliment. He blamed Hislop for public cynicism towards politicians, arguing that "even satirists are citizens, too. They surely have to at least consider whether what they do is harmful as well as enjoyable." How does Hislop plead?

"It's very flattering to be told you are powerful, important and malign, but it's an old argument. All satirists have been told, 'You're making the job of government impossible' when all we are really doing is trying to keep them honest. Of course their job is difficult, but it's better to say that these things are going on than say, 'This is a tough job, give them a break.' That leads to Italy or Greece." He insists he doesn't condemn all politicians. "We have politicians to lunch, we talk to them, they give us stories, if they lead a campaign we support, we give them credit. But this is not the time – so soon after the expenses scandal – for satirists and journalists to leave them alone. I don't think the public would thank us for that."

I ask Hislop if he is a good hater. It is one of the few questions that makes him pause. "I don't recognise that," he says eventually, before contradicting himself by pointing to his pet hates. "I did hate Maxwell, and there are various people I get obsessed by. I got obsessed by Brown, just watching him in the Commons exploding about News International. The sheer humbug of it. The man who had Wendi [Deng, Rupert Murdoch's wife] for a sleepover complaining about News International. It was unbelievable. So I'm capable of that kind of focus, but then afterwards I think, 'Why are you quite so bothered by that?'"

Newman defends his partner against Kettle's charge. "Ian has a reasonable and moral core. He's interested in double standards, but he doesn't put the boot in without thinking about it."

"He [Hislop] kept a story out of Private Eye recently," Wheen adds, "because he thought the person it was about was a bit mentally fragile, and he didn't want to be responsible for him doing any harm to himself. But he is also very combative when it comes to taking on corporations and institutions – those who can look after themselves."

While Hislop can be a formidable adversary, he is also a very good ally. "Once you're a friend of his, you're a friend for life," Newman says. "I've said things about him in the past that I probably shouldn't have, but he's very forgiving."

"He's always been terrifically nice to me," Wheen agrees. "When my marriage broke up in January 1993, for example, I had quite a rough time. I was essentially homeless, living in someone's attic. Ian was fantastically solicitous. He kept asking if there was anything he could do, offering to help financially. He's an absolute rock."

At Private Eye, Hislop is a practising Anglican surrounded by atheists. He says it is a misconception to assume satirists must be radical. "Swift was a dean in the Church of England. Byron was a member of the House of Lords and never gave it up. Conservatives are suspicious of what's happening, and if you're enthusiastic about what's happening, which is the traditional, optimistic, liberal position, you're less likely to say, 'It's rubbish.'"

The Anglicanism, his love of history, the documentaries he makes on railways, the first world war, the Scout movement, Victorian philanthropists are all of a piece. He has a strong sense of what constitutes ethical behaviour and the good society, and is not slow to castigate those in public life who fall short. It is not that he despises politicians that makes him so severe on them, but that he holds in such high esteem what they can be at their best.

According to Newman, with whom Hislop has written TV series, a film and radio programmes, as well as countless jokes for Private Eye, his fogeyism is reflected in his attitude to sex. "Ian's quite squeamish about it," he says. "Private Eye is full of smut, but when we wrote a film a few years ago and the script editor wanted to put in a scene where the hero walked around the house naked, Ian was very against it. He just thought, would he want his children to see that he'd written that?"

Hislop's conservatism extends to the future of the media, and he does not foresee Private Eye embracing the digital future. It has a rudimentary website, but keeps its key content for the magazine, and he gives me a brief lecture on the dangerous culture of free. "What am I meant to do with the people in there?" he asks, pointing to the production department. "Are they meant to work for nothing? As a model it seems to me to be ludicrous." But won't someone eventually produce a satirical website that undermines the Eye? "Possibly, but I'm not going to try to do it in order to prevent that. I want to go on doing the same thing. Obviously. That's my personality defect."

Hislop won't tell me how much profit the Eye makes, but its circulation is well above 200,000 – higher now than at any time for almost 20 years – and it's far from lavishly produced or generously staffed, so one can assume a healthy bottom line. The downside is that it needs to keep a large contingency fund for legal losses. Even when it wins, there is always the danger of losing. Accountant John Stuart Condliffe fought a decade-long battle against the Eye in the courts, dropped the case, declared himself bankrupt and left the magazine to pick up a bill for £1m in costs. "The public imagine that when you win, you get your costs back," Hislop says, "but you don't."

He shows no signs of stepping down, and unlike Ingrams has not identified a member of staff he wants to inherit the crown. Wheen says he can't imagine who would take over. "It's quite hard to find someone who can juggle cartoons with one hand and writs with the other." He wants Hislop to carry on for another 25 years. "That will probably see me out. By then, some child as yet unborn will be taken away and raised in a monastery in the traditional way to edit the Eye."

• Private Eye: The First 50 Years is published by Private Eye Productions at £25. The exhibition of covers and cartoons is at the V&A's Studio Gallery from 18 October-8 January 2012.