It's not often you go to the bar during the interval of a play and overhear Ewan McGregor asking his friend if “that was a real baby that Hamlet just carried on stage”. Yet in a production of Shakespeare as unorthodox as the Factory's, people are bound to get confused. It was indeed a genuine newborn, plucked from its mother's arms, though it must be said she looked delighted.

He might be a veteran actor, and on a night off from starring in Othello across town, but McGregor is as surprised as any other audience member by the turn of events this Hamlet is taking. How can we remain so tense while Gertrude is poisoned by smeared chocolate cake? So thrilled as Laertes warns Ophelia about men's wicked ways while toying with a bulky marrow? So genuinely terrified as Hamlet and Laertes duel over who can read the loudest from a leaflet?

All these props are plucked at random from the audience, who are reseated at the start of each act as the actors progressively take over the chairs, the bar and the corridors. Oh, and the cast decide who will play which part only as the performance begins - they have all memorised several.

It's a rare feat for a play to use such gimmickry to create real profundity, yet it works - McGregor tells me afterwards that it was “just the most amazing thing to see. Brilliantly directed, brilliantly played, brilliantly executed. I thought it was incredible - and terrifying. I mean, can you imagine not even knowing if you're going to play Hamlet or not?” Yet without McGregor it might not be happening at all.

Alex Hassell, 27, co-founder of the Factory theatre company, explains how the A-list actor got involved with these fledgeling stars. Hassell was rehearsing for a show at the Globe in early 2006 when McGregor, who happened to be walking past, grabbed him to say that he and his wife had loved the BBC3 comedy show that Hassell had starred in, Bonkers. “But they'd missed the last episode, so I sent him a video of it and then thought, well, why not enclose a letter about this theatre group I'd started up with my friends, see if he likes the sound of it.”

The Factory was set up because, on leaving drama school, Hassell and the group's co-founder Tim Evans, also 27, “wanted to know why all of our mates, who were brilliant, were still so frustrated. “Acting's not like writing, you can't just do it in isolation, you need a part. But the repertory system isn't what it was,” says Hassell.

As it turned out, McGregor did indeed like the sound of it - and sent them a generous cheque. Delighted with this unexpected cash injection, the actors realised they could try other wealthy stars for donations, especially since the Arts Council had turned them down. They don't wish to name too many names, but Elton John was another who came to their aid. And with the esteemed actors Bill Nighy and Mark Rylance agreeing to be patrons, it seemed they were all set. But why do they make their performances so difficult for themselves?

Evans says: “We want to do the total opposite of what people think they need to do to get a good show on, which is get it in the listings, get a good review and sell all the tickets before the day.

“We don't want to be listed in Time Out, really. And a review is pointless because you will only be seeing one production out of endless different ones. We're never going to do a press night. We ask, what has become accepted as necessity in the theatre? And then scrape those things away, to see if you don't need them to put on great performances.” Of course, they didn't really mind when one paper [London's Evening Standard] reviewed them anyway, calling it: “a theatrical coup ... unbearably poignant, unrepeatable” (and clearly won't mind any publicity generated by this piece either).

The Factory perform Hamlet at 5pm every Sunday, somewhere in London, preferably hijacking a theatre stage currently dressed for a different production. Word of mouth or an e-mail announcement a few days before are the only ways of knowing where it's on. Audiences are given badges so they can recognise each other later, like a secret society - I've already been spotted with mine. Every ticket costs a tenner and the cast are a big revolving group of unpaid actors, so if anybody is away working, the show will go on.

As Evans explains: “Most young theatre groups will stage one production and it's an immediate endgame. Rehearsing for weeks for a five-night run in a small theatre, nobody really comes to see it and afterwards they're right back in exactly the same position they were in before - stuck and frustrated again. So we thought long-term.”

They workshopped this Hamlet for a year first, having taken their inspiration from their main director, the Globe's former associate director Tim Carroll, who invented the main premise of the production while working in Hungary in 2005. “When I rehearsed Hamlet in Budapest,” says Carroll, “I often found that some of the actors were unavailable. I didn't care: I just rehearsed with whomever I was given. Because I had four Horatios, two Poloniuses etc, there was always something I could work on. In this it was more like training a football team than rehearsing a cast.”

There is a trend towards this deconstructed method of audience involvement, with the Punchdrunk group's radical productions of Faustus and The Masque of The Red Death making audiences chase around after the cast. But the work of the Factory feels more welcoming to the paying guest. Even McGregor says that, while he tries to aim Iago's soliloquies directly at some- body in the Donmar's audience, he can't hope to get as close as these guys can.

The Factory liken their methods not to theatre companies but to Radiohead, who have escaped their major record label by distributing their album online and announcing their gigs by e-mail on the day they happen, or to the guerrilla graffiti art of Banksy, or flash mobs. Indeed, their dream is to have Jonny Greenwood from Radiohead strumming guitar on stage, while Philip Seymour Hoffman, just passing through town, takes on a part. It might be a pipedream - “but then we thought that about having a beer after our play with Ewan McGregor”. Watch this space. Or, for that matter, updates on the website below

www.seehamlet.co.uk

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