How much would you pay for 10 minutes of theatre? £2? £3? Maybe even £5, if the actors ask really nicely? Might you decide to pay nothing at all?

These are some of the questions posed by Bush Bazaar, an intriguing interactive show, conceived and produced by the theatre company Theatre Delicatessen, which on Tuesday night takes over the Bush theatre's new building in west London. For three weeks, 22 theatre groups, comprising more than 100 performers, will be occupying the theatre's every nook and cranny, waiting to pitch for your custom: after paying your entry fee, you will decide how much to pay for each performance. You can wander the building, bartering and haggling for the actors' time, as if over spices or rugs in a crowded north African bazaar.

At the show's heart is the timely question of value: of money, of course, but also the value of theatre – how much we are prepared to pay for it, and what effect that decision has on our relationship with what we see. Roland Smith, one of Theatre Delicatessen's three artistic directors, explains: "We wanted to do something in response to the crash: less about what actually happened, and more to do with the concept of transaction, of the marketplace. Then the repercussions of that, and their effects on arts funding. We wanted to explore 'what is the value of art?' "

This isn't the first time that Smith and his co-directors, Jessica Brewster and Frances Loy, have mounted a show like this: their 2010 piece Theatre Souk did much the same thing, installing young theatremakers all over the company's then headquarters, the former Uzbekistan Airways building in London's West End, and asking them to barter with their audience.

Bush Bazaar is, in effect, a reprisal of this show, which they also plan to stage again in their own building in the autumn – but the fact that it's taking place in a mainstream theatre shows just how far Theatre Delicatessen, more often known as Theatre Deli, has come since four young people (producer Mauricio Preciado Awad has since moved on) first got together in 2007.

Their intention was to mount large-scale, immersive theatre in the only spaces they could afford: empty office blocks awaiting dereliction or resale, which they would occupy for a peppercorn rent and a limited period, turning those ghostly buildings into living, breathing arts centres.

Their first base was a disused workshop on Regent Street: there, in 2009, Theatre Deli created the acclaimed Pedal Pusher, a true-life story of three cyclists doing battle for the Tour de France. Next up was the Uzbekistan Airways building a few streets away; here, true to the company's name - chosen, Smith says, to show that they want their theatre to be "quality, fresh, organic; plus we want a deli on every corner eventually" - continued to produce a diverse range of shows, including an all-female version of A Doll's House.

Theatre Deli's present home is the old BBC London building in Marylebone, a labyrinthine series of corridors and abandoned recording studios. Here, under the name Marylebone Gardens, Smith, Brewster, Loy and their collaborators are building a flourishing artistic community. There's a basement performance space, where the company's superb, Falklands-inspired production of Henry V has just finished; an "indoor garden", turfed with artificial grass, with a big screen for Olympics-watching; and upstairs, a warren of studios and rehearsal rooms, available to artists and other freelancers for a reasonable fee. Theatre Deli is also offering space to promising young theatremakers in exchange for a few shifts on reception.

The building functions, in effect, through a system of bartering – just like Bush Bazaar. The show's themes also reflect the way Theatre Deli has had to negotiate its temporary tenancies (a complex process, for which it enlisted the help of property developer James Bowdidge), and sources of funding (only one of its eight shows, A Doll's House, has ever been awarded money by Arts Council England, so the troupe has had to find ingenious ways of balancing the books). "We're working with commercial property developers, City lawyers, investment banks," Smith says. "This idea of the bazaar mirrors the sorts of deals we have to do every day."

So entrepreneurial is Theatre Deli that its very success poses a worrying question: are the cuts to arts funding in fact justified, if young companies like this can function perfectly well without it? Brewster looks pained: "The fact is that we still have to do other jobs," she says (each of the directors works full-time; Brewster and Loy also have two children apiece). "If I were being petulant about it, I'm almost at the point where - to the big funding bodies, mentioning no names - it is like, 'Can you please come and look at what we're doing, who we're housing here, and who we're giving opportunities to?' We need some support, because to be completely honest, we are coming very close to a line."

Smith adds: "Nobody's ever walked up to me and said, 'you know, what we really need you to do is put on theatre'. It's completely our choice; and I think we need to find our own way of making work." Brewster nods; then says firmly, "That's why, for us, this year is really about money." What better show to hammer that point home than one that puts the value of money firmly in the foreground?

• Bush Bazaar is at the Bush theatre, London W12, from 31 July to 18 August. Tickets: 020 8743 5050 or bushtheatre.co.uk. Shows continue at Marylebone Gardens all summer; for more information, see theatredelicatessen.co.uk