Entering a deserted tower block certainly brings back a few memories. When I was younger and poorer I visited many, perpetually searching for a new place to squat. Once the police stopped a small gang of us and asked where we were going with that crowbar. “We borrowed it from a mate and now we’re giving it back,” we replied, and they could do nothing for it was the truth (and we were white).

This 20-storey monster is St Catherine’s House in the Beaumont Estate in Leyton, the grittiest part of a tough area of East London. Lying between Walthamstow and Stratford, it may even be the nearest thing to the “Walford” of EastEnders. The estate has three soon-to-be- demolished high rises, its own gang, the notorious Beaumont Crew, and, for a few weeks, its own theatre. As part of the Beaumont Project, funded by the Carnegie Trust, the enterprising Offstage Theatre company is staging Home, a piece based on the memories and stories of the residents, in an empty flat. (At present eight families still remain in the block.)

“What’s more magical than the space where stories were lived?” enthuses the director and co-writer Cressida Brown, who heard about “these grim towers” when searching for a performance space. No 14 has been decorated with pictures by children from the local primary school, several random items left behind by the previous occupants and some eerie wall paintings, including a representation of a local kid’s nightmare of falling from the roof. A teenager’s room has been transformed by a local graffiti artist.

A dozen or so of us are collected urban-safari-style at Walthamstow Central and packed into a minibus. On arrival, we follow a cast of four through the corridors.

Site-specific productions are increasingly common, straddling the line between performance art and conventional theatre. In the past few months London punters could enjoy a trip to the disused baths in Soho’s Marshall Street (Deep End) and even a piece acted out on a bus (Last Tuesday). Home’s producer and co-writer Elayce Ismail points out that such stagings “always try to present something new, rather than just a revival”.

People are interested too. Tickets to the show, which runs until February 4, are already sold out, except for those reserved for residents. Everyone from the BBC to specialist architecture publications has covered the event. “It appeals because it’s going soon,” says Brown, referring to the piece-by-piece demolition that starts next month.

Truth be told, Home is not much of a play at all, though the cast of four are well up for it in the unusual domestic surroundings. The narrative follows a single mother and her two teenage kids. Something bad — we’re never told what exactly — has happened involving the daughter’s dodgy boyfriend, but was she implicated? It makes for an intriguing slice of social history, though. The dialogue is pieced together from real recollections such as laments about poor soundproofing and the impossibility of eavesdropping on neighbours who argue in an unfamiliar tongue.

The 2012 Olympics and the much loved Swiss Re building (aka the Gherkin) are mentioned, both ever present to East Londoners. Lines about clinging on to leaves and flowers might seem corny to hardened capital cynics, but they are genuine and heartfelt.

No wonder that an audience member, Shirley, a Beaumont resident for 40 years, had tears in her eyes. At times she was seeing her own words being performed.

For a few nights, though, the sleepy borough of Waltham Forest actually has a theatre of sorts. The borough where Alfred Hitchcock was born no longer has a cinema, while Walthamstow, its centre, is best known for its dog track. A recent attempt to regenerate the heart of the “Stow” around a proposed Will Alsop library development foundered on financial grounds. Some officially sanctioned pranksters from the local art college left their mark on the cleared site, erecting a sign describing it as the location of the future “Guggenheim Walthamstow” and even featured a fanciful illustration.

Some might consider the encapsulation of 40 years in an hour patronising, but is the alternative to let buildings, even whole districts, disappear unremarked? Brown has been heartened by the positive response of even the most sceptical locals. She can take the idea elsewhere too — “All over the world,” she says. The Middle East alone should offer possibilities for years to come, not to mention ill-considered proposals to destroy entire neighbourhoods in the north of England. Wherever people are displaced, Offstage can commemorate them. Perhaps they should franchise themselves.

Sarah Vine wll return next week.