Down a narrow side street near Waterloo station, hidden from the tourists and London commuters behind tall wooden doors, is the relic of a bohemian dream.

Behind the doors are a tennis court, a lawn and park benches. A children’s swing set and seesaw are painted a fading mustard and tomato red. The residents whose windows look over this rare sanctum live in one of Waterloo’s nine housing co-ops – an unlikely bit of social housing in this coveted slice of the city.

But the peace and quiet is under threat from an unlikely invader: Abba.

Or, more accurately, Abba’s fans. Former band member Björn Ulvaeus wants to build a branch of his themed restaurant Mamma Mia! The Party here. The “singing theatre” concept, based on the film musical, already has a flourishing branch in Stockholm.

The plan is supported by Coin Street Community Builders (CSCB), a social enterprise developer that built four of the nine co-ops in Waterloo and is offering to lease the land on Stamford Street to Mamma Mia! The Party for five years. But many local residents have objected, saying they don’t want to surrender their neighbourhood to crowds of raucous Abba fans every night. Posters in the area warn: “Five hundred drunk revellers will spill on to these streets singing Dancing Queen.”

Former Abba member Björn Ulvaeus at the Stockholm branch of his themed party restaurant. Photograph: Jonathan Nackstrand/AFP/Getty Images

This will be upsetting for Ulvaeus, who has described the South Bank as “the perfect place” for his restaurant, and suggested that the building could host other activities outside what he calls “party hours”. “We hope it would be an asset for the whole community,” he says.

Unfortunately, the whole community doesn’t agree. “Most people here have nothing against Abba,” says Ken Smith, who lives in Edward Henry House, opposite the proposed site. “We were in the generation that was brought up with Björn and the girls. The problem is the disruption.”

Residents have also accused CSCB of losing its focus on social housing.

To visitors, Waterloo is a cultural playground. The reclaimed marshland boasts the Old and Young Vic theatres on the Cut, as well as the National Theatre, Queen Elizabeth Hall, Hayward Gallery, British Film Institute and other attractions beside the Thames. At its heart, however, are the co-ops. Here, rents are as low as £124 a week for a two-bed unit – far below the market rate for central London.

The co-ops had their genesis in the 1970s, when Abba were clocking up number ones and the area was a “patchworky wasteland”, as resident Karen Philipp describes it.

A Coin Street protest in the 1970s targets the Greater london Council (GLC). Iain Tuckett pictured centre.

When office developers began eyeing the South Bank, Waterloo’s residents objected that some of it should be saved for social housing. The protests came to a head in 1977, when the Coin Street Action Group won the rights to the land to build a co-op housing community.

Four years later, after public inquiries, the land was eventually divided, with 13 acres going to the housing activists and the rest to developers. (The £750,000 paid for those 13 acres in 1981 might now buy one house in the area.) Coin Street Community Builders continued to add co-ops into the 2000s, and now owns and manages – among other things – four co-ops, Gabriel’s Wharf and Riverside Walk, the Bernie Spain sunken gardens, the Stamford Street Neighbourhood Centre, and the Oxo and Rambert Dance Academy buildings.

Born out of protest, the co-ops are still hotbeds of activism. Having successfully fought the Garden Bridge project, residents are now opposing what they see as a creeping commercialisation of CSCB’s activities. They are particularly incensed by plans to build apartments, a leisure centre and a public swimming pool on Doon Street, next to the National Theatre. The development would include a 43-storey tower. CSCB is contemplating setting part of it aside for co-op units, after criticism of its entry into the conventional housing market. Some locals also complain that other CSCB ventures, such as a nursery with its own chef, are too high-end.

“What’s happening with these community ventures is that they, by and large, are not used primarily by the community,” Philipp claims. “They are used by local businesses.”

A Coin Street community housing scheme behind the Oxo Tower. Photograph: Alamy

Meanwhile, says Lambeth councillor Kevin Craig, who presented the council with a 745-signature petition against Mamma Mia! The Party, “residents on normal incomes and living normal lives are increasingly finding it hard to get heard”.

CSCB, not surprisingly, sees things differently. “I get that people feel a pride about our whole area and they want to keep it good,” says board member Iain Tuckett, who has lived in Waterloo since 1974 and was convenor of the original Coin Street Action Group. The debate is “healthy”, he says, but the site proposed for Mamma Mia! The Party was never destined for social housing, and once the restaurant closes, CSCB plans to use the land to extend the neighbourhood centre. While most of the co-ops on Stamford Street are set back from the road, he adds, the kerbside position of this spot makes it “inappropriate” for homes.

As for the claims that CSCB has become too commercial, Tuckett believes there is a misunderstanding about how Waterloo’s co-ops were paid for: “The last co-op needed a cross-subsidy from our commercial bit of £3m – and that wasn’t money we had in our pockets. We had to borrow against future commercial income revenue, otherwise we couldn’t do it.”

The Mamma Mia! The Party team don’t want to get drawn into the debate about social housing. “We were absolutely shocked to discover that there was this little disagreement among the community,” says Ulvaeus’s co-director, Ingrid Sutej. “But that’s not something we could comment on … I think that’s between Coin Street and the local [residents].”

She does say, however, that they are trying to address the community’s other concerns: they will fully soundproof the venue, and while the show was originally planned to finish at 11.30pm – and later on weekends – they have since pared that back by an hour. They have even engaged the crowd manager who handled London 2012, and are promising jobs and apprenticeships to locals. “We’ve gone to great effort and care to be as friendly and neighbourly as we can,” says Sutej.

It remains to be seen whether that will be enough to win over the critics. Lambeth councillor Jennie Mosley lives behind the proposed Mamma Mia! The Party site in the Iroko co-op, a sleekly designed collection of boxy units bursting with balcony gardens, arranged in a horseshoe around a children’s playground. CSCB has made this “a great place to live”, she says. “People are just really frustrated about this piece of land being used for Mamma Mia, and not for the development of social housing. I fear I’ll be living with Waterloo being screamed out every night at 11 o’clock.”

Follow Guardian Cities on Twitter, Facebook and Instagram to join the discussion, and explore our archive here