Mention the phrases "surely shome mistake", "that's enough, ed" and "Ugandan discussions" and you instantly know what territory you're in – the world of Piers Moron and Peter Carter-Fuck and a satirical magazine born almost 50 years ago, on 25 October 1961.

Originally six pages printed on yellow paper, Private Eye is still put together by the editor shuffling copy printouts around a proof page. These scrapbook pages are now electronically subbed using modern software but up to 2000 the Eye used the old-fashioned system of printing out copy, pasting it onto boards and then photographing them.

And the eccentricities don't end there. The Eye, as it likes to be known, still holds its legendary lunches at Soho's Coach and Horses pub, where fish pie or fish and chips is eaten, wine drunk and gossip shared with editor Ian Hislop, his deputy Francis Wheen, Hislop's predecessor Richard Ingrams and other Eye hacks. It's just around the corner from the fortnightly title's Carlisle Street offices, a ramshackle converted townhouse bedecked with dusty old papers and cartoons on the wall, where the identities of its many contributors (between 150 and 200 payments are sent out for each issue) are closely guarded.

The magazine still prints a photo of a lookalike of Hislop in the letters pages whenever he's away on holiday, and it continues to find any excuse to print an old snap of Andrew Neil in a vest at a disco, with a pretty companion half his age. Private Eye's ideas of "new boys" are joke writers Tom Jamieson and Nev Fountain, who have been there a mere 10 years.

There are other traditions, as revealed in Private Eye: The First 50 years, by in-house reporter Adam Macqueen and published next week – such as senior staff falling out with each other and then making up, starting with the firing in 1963 of the first editor, Christopher Booker.

He returned two years later, only to leave again in 1976 after the Eye had been rude about two friends (one of whom was Arianna Stassinopoulos, now Huffington). "On its day [the Eye is] a strong candidate for the most unpleasant thing in British journalism," he wrote in the Spectator shortly afterwards. He wasn't away long.

"Can you imagine a journalist leaving a newspaper, writing that and then returning?" asks Macqueen, who has worked for Lord Gnome for 14 years. "But the Eye is a bit like a family – you can behave terribly and do the most unforgivable things and yet you still get along and meet up at Christmas. It's also a family that is made up mostly of funny uncles."

But what may seem to some an affably quirky and semi-amateur operation (one where Ingrams still refers to the in-house accountants as "box wallahs") is a very successful business which is bucking the trend of the decline of print media.

Subs support

The Eye's first MD, Peter Usborne (who went on to found the flourishing Usborne Publishing in 1973), was one of the first to spot the importance of subscriptions to a magazine business model, and of relying on cover sales and not advertising to increase profits. Subscriptions may get regularly cancelled by irate letter-writers but the current tally of 113,000 subscribers has never been higher and only about 10% of turnover is reliant on advertising.

Circulation overall is at an 18-year high with fortnightly sales around the 206,000 mark ("like John Terry's shorts", Hislop notes, "in the past they may have been down – but now they are firmly up again"). And in recent weeks they've been even better – a special hacking edition in July with a "Gotcha! – Murdoch goes down with all hacks" cover shifted 253,000 copies. Pressdam, which owns Private Eye, made a profit of just over £210,000 in the 12 months to September 2010.

The magazine is "very careful about its costs", says finance director Geoff Elwell, with seven staff journalists working on a one week on, one week off basis, alongside eight production staff and five joke writers. "Not even the editor has an expense account," he adds.

The team are also proud that the magazine hasn't increased its £1.50 cover price for five years. Neither would managing director Sheila Molnar countenance going down the route pursued by "some publishers" and selling data on its subscriber base: "We have a loyal readership and we would never make short-term gains that way," she insists. "It's not what Private Eye is about."

What the magazine is about – its identity – is, to a large extent, shaped by Hislop, who insists that the Eye should always strive to be "a bit better than the people you write about".

His tenure has been notable for fewer libels, a greater insistence on accuracy, and getting rid of both sex stories ("they seemed to amuse Richard [Ingrams]," says Macqueen) and what Hislop has dismissed in the past as "social gossip". His Eye sets its sights at genuine corruption or hypocrisy or mendacity, rather than offering tittle-tattle.

With almost no bylines in the magazine besides the likes of Lord Gnome, Glenda Slagg, Dr B Ching, Remote Controller and Lunchtime O'Boulez, Hislop seems content to be its public face, as was shown when he led the charge in fighting Andrew Marr's injunction in April – a point of principle which cost Private Eye six-figure legal bills and produced only a few paragraphs of copy.

Despite almost constant speculation (sometimes from people wounded by Eye stories), Hislop is clearly staying put. "Another 30 years should just about see 'em off, ha ha!," he notes in Macqueen's book. "I have no plans at all to leave." Some staffers suspect that when the time comes to go he may leave it to another young buck (he was 26 when he took over) – someone who, one jokes, could take the Eye "into at least the last century digital-wise".

But does it need to? For many insiders, the title, whose only concession to modernity and digital media seems to be the dissemination of a few Twitter-friendly headlines for each issue, can afford to remain a largely print-only offering. Molnar says possible iPad apps have been examined and "none of the options have proved satisfactory so far". In any case, there's a determination not to give the Eye's content away free. "We can't afford to," says Elwell.

A digital subscription would almost certainly boost overseas revenues, but the Eye's managers are firmly sceptical. "There isn't anything that we have seen that delivers what we want to deliver," says Molnar. "People who have the Eye like screwing it up and taking it out with them or reading it on the loo. Can you imagine people rushing over to someone and showing them this brilliant cartoon on an iPad?"

Cartoonist and joke writer Nick Newman – one of Hislop's oldest friends, and co-writer with him of radio and TV comedies – agrees: "I'm unimpressed with the digital humour media – it lacks the scrapbook feel of the Eye, where the funniest joke of the week rubs shoulders with a piece about eco-farming."

Staff are also doubtful whether Apple would allow them to show some of their more risque material. "Would we be allowed to have a picture of Rebekah Brooks with her top off?" asks Molnar. This was the image of the former News International chief executive mocked up as a Page 3 girl which recently led to a long-time subscriber in a US penitentiary having his copy confiscated on obscenity grounds.

Youth appeal

"Around a quarter of readers are 30 or under and our readers' average age is 43, which is younger than you might think," says Molnar. "I do get letters from 85-year-olds saying they can not read the print any more but a large number of our readers are in their 20s."

But many at Private Eye want more female readers, who make up only 30% of the total. And they agree with Newman that the nation and the magazine need new young cartoonists ("The youngest we publish now is, I think, 41," he says. "Blimey – where are they all? I was sending stuff in when I was 17.")

But staff remain confident that it can continue to hook young readers – and keep them. "So many people have it at home when they are young, they read the cartoons and gravitate to other, perhaps more serious areas as they get older," says Molnar. "I came to the Eye as a student reading Paul Foot and for me it's all about the content."

Macqueen agrees. "The end of the Eye will come when all politicians clean up their acts, when the workings of Whitehall, the media, the justice system and everything in between become entirely transparent, when the British lose their sense of humour and rediscover the deference due to their elders and betters and a herd of Gloucestershire Old Spots fill our airspace. And even then, we'd probably still find some excuse to print a picture of Andrew Neil in a vest."

Private Eye: The First 50 years, an A-Z by Adam Macqueen, is published on 20 September by Private Eye Productions. The Private Eye Display at the V&A runs from 18 October to 8 January. Entry is free.