Agatha Christie's whodunnit is 60 years old. What's the secret to its longevity? Stephen Moss goes behind the scenes, into 'the snow room' and off to the pub for a sing-song with the cast

Quentin Tarantino came to see The Mousetrap two years ago. I wish I hadn't been told this, because when I recently caught the play, which this week clocks up its 60th year in London's West End, I couldn't help wondering what he might do with Agatha Christie's creaky old detective story. Blood, gore, black humour, circuitous chatter. It could be wonderful, although it would probably only run for a fortnight.

I had always been fascinated by The Mousetrap, which was at the Ambassadors theatre for 22 years after its premiere in 1952, before moving next door to the atmospheric St Martin's. I had registered the annually changing sign on its facade – "60th year" it trumpets today – and wondered about the clusters of Japanese tourists outside. But I had never seen it until last week, when, to mark the joint celebration of its 60th birthday and its 25,000th performance, I saw it not once but three times.

A Tuesday matinee is probably not the best place to start: 100 or so devotees in a theatre that seats 550. The first thing you notice is a wooden sign in the foyer: "This performance is number 24,993 of Agatha Christie's The Mousetrap, the world's longest-running play." Many of the audience have themselves photographed with it, claiming their place in theatrical history.

A young woman is outside with her grandmother, who uses a wheelchair. They ask a man in a suit for a ramp, thinking he is staff. He isn't – he's here to see the play –, but goes off to find one anyway. We are, after all, one big family. Linda Allcock, down from Birmingham with her husband, Roger, is celebrating her birthday. "I've always wanted to see The Mousetrap," she tells me later, at the interval. "So I said, 'Right, I'm 60, it's their 60th anniversary – I'll go and see it.' I love Agatha Christie." I ask if she has worked out who did it. She hazards a guess. I tell her she might be in for a surprise. "Was it a member of the audience?" chimes in Roger, a brilliant suggestion.

There are eight members of the cast, each signed up for a 47-week stint. More than 400 actors have appeared in it over the years. Richard Attenborough was the original Detective Sergeant Trotter, and his wife, Sheila Sim, the first Mollie Ralston – owner of Monkswell Manor guesthouse, which inevitably gets snowed in (this doesn't stop Trotter, who arrives on skis to tell the residents there's a murderer close by). But apart from Attenborough and Sim, few players have been headliners. The Mousetrap is not a star vehicle; the play and its author are the stars.

The counter displaying the tally of performances to date

The drama became the longest-running show in British theatre history as early as April 1958 (plays back then didn't run for as long as they do now). From that point on, says producer Stephen Waley-Cohen, "it began to develop its own momentum". They liken it to Madame Tussauds and the Changing of the Guard – something you have to catch if you visit London. But the audience is not, as conventional wisdom suggests, made up mainly of foreign tourists. The majority are from other parts of the UK; for them, The Mousetrap is part of the London experience. It's like some quasi-religious ritual, with the audience as much a part of proceedings as the cast.

Geoff Bullen, the current director, accepts it is a rite of passage, but insists it works as theatre, too. "The play is substantial and the characters not just cardboard cut-outs," he says. "It's wonderfully structured – up there with A Midsummer Night's Dream." Charles Spencer, the Daily Telegraph's theatre critic, sees it more as a midwinter afternoon's nightmare. "The St Martin's theatre is one of the most attractive playhouses in the West End," he wrote last year, "and it is tragic that it has been filled with such tedious tosh for so long." Telegraph readers, the play's natural constituency, rounded on him.

Rather than a sleepy November matinee, perhaps I should have opted for the current touring version at Southampton's Mayflower, where it played to 2,000-strong houses for a week. "Audiences have been attentive and focused," says Ian Watt-Smith, director of the touring show, "with lots of laughs as well as oohs and aahs at the reveals." The 60-week tour has been arranged to coincide with the anniversary, but it's a one-off: St Martin's likes to protect its property, expecting theatregoers to come to London to see it. This also explains why there has never been a film.

The play is a curious mixture of 1950s drawing-room comedy and murder mystery. The key, says Watt-Smith, is not to send it up. "You have to concentrate on the reality of the situation. Everyone is trapped in this guesthouse – they have no means of contacting the outside world, and the murderer is among them. No one is quite what they seem. They all have secrets. You have to encourage the characters to play the real backstory and then cover it up, which is a challenge."

Waley-Cohen adds: "It works because it's in period and it's done absolutely straight. It's not knowing or camp." But given that most people go to see it as a phenomenon rather than as a play, surely there's an awareness of its historical baggage? "A little," he says, "but more on the part of the audience than the cast. We hope the actors are playing it as if it was a new play set in 1950."

The next evening, I see The Mousetrap again, but this time backstage, sitting with the actors. They make me feel very welcome, showing me the "snow room", where every visitor to Monkswell Manor gets a heavy coating of white flakes (made from carpet foam) before going on stage; they even offer to let me crank the historic wind machine (as used in the original production) and take me to a Soho pub afterwards for their traditional Wednesday night sing-song.

"I like the idea of being part of this great theatrical continuum," says Anne Kavanagh, who plays snooty Mrs Boyle. Natasha Rickman, who graduated from Rada last year, can claim even closer allegiance to that tradition: she is playing Miss Casewell, as her mother, Miranda Bell, did in the play's 33rd year. "She came and saw me on the first night," says Rickman, "and said it was a weird experience."

Actor Michael Fenner eating dinner backstage before a performance

Andrew Bone, who makes an admirable job of old buffer Major Metcalf, says one reason he took the part – apart from guaranteed work for a year – was "the chance to see this thing called The Mousetrap from the inside". His conclusion? "With a Thursday, Friday, Saturday audience that are up for it, you don't hear the play creaking and it can really take off. When you get a quieter audience, you can hear it creak."

Bone and some other cast members are writing Mousetrap spoofs, which they perform for their own amusement. He says they will come in handy in February, when the cast is six months in and hitting the theatrical equivalent of the marathon-runner's wall. In them, the characters Giles and Mollie become Miles and Polly, while Mrs Barlow, the unseen daily help, is fleshed out. I imagine these send-ups are brilliant – could Mrs Barlow be the murderer? As Tom Stoppard demonstrated with his early play The Real Inspector Hound, about two theatre critics who get caught up in the preposterous country-house murder mystery they are watching, The Mousetrap must be the most spoofable play ever written.

A few days later, I get a taste of what an alternative Mousetrap might be like. At a gala charity evening to mark the 25,000th performance, an all-star cast – including Patrick Stewart, Julie Walters Iain Glen and Miranda Hart – perform a reduced version, running to 80 minutes rather than two hours. They are clutching scripts and have had hardly any rehearsal, but give a spirited account that points up the comedy. Sudden death seems even more inconsequential than usual.

Just before the gala, a memorial to Christie is unveiled close to St Martin's by her grandson, Mathew Prichard, to whom she gave the rights to The Mousetrap for his ninth birthday. What a present! The statue, a bronze bust of the author set within a book, is monolithic and apparently immovable, but whether it will outlast her creation is a moot point. The Times, in a leader this week headlined "Mystery of The Mousetrap", anticipated the day when the show would finally close. But will that day ever come?

"I don't want to be the man who took The Mousetrap off," says Waley-Cohen. "And I don't think I will be. Managed properly, I think it will run for ever."