The proud slogan of the Conservative flagship council of Hammersmith and Fulham is "Putting residents first". But campaigning residents of two council estates in the west London borough believe that David Cameron's favourite local authority cares little about what they want.

"We are the wrong sort of people in the right sort of postcode as far as they're concerned," believes Sally Taylor, who chairs one of the estates' tenants and residents associations. "We're sitting on a golden nugget of land. They've never thought for one minute that we're human beings."

Her words prompt nods of agreement from those sitting with her around a table at the Gibbs Green estate's community hall: nine women and two men who have gathered to plan a summer festival.

The bad blood flows from the council's wish to knock down these people's homes. Gibbs Green, completed in 1961 and the adjoining early-70s West Kensington estate, the one Taylor represents, form the neighbourhood next door to the Earls Court exhibition centre.

But the two estates could be bulldozed after the 2012 Olympics, as part of a huge regeneration scheme that Hammersmith and Fulham is working on with developers Capital & Counties. The council argues that this will revitalise the Earl's Court area by creating new jobs and a virtuous "mixed community" in place of an unhealthy dependency culture. Diana Belshaw, chair of the Gibbs Green tenants association disagrees. "If the estate is pulled down, the community spirit will be killed," she says.

The stand-off crystallises a tension between different layers of Conservatism in power. Hammersmith and Fulham's leader, Stephen Greenhalgh, argues that his regeneration strategy – rather pointedly entitled Decent Neighbourhoods – which envisages the levelling of several other council estates as well as Gibbs Green and West Kensington, exemplifies a harmony between good business sense and beneficial social outcomes. Yet an element of Cameron's "big society" strategy might enable residents opposed to demolition to save the estates by taking ownership of them.

The Department for Communities and Local Government wrote to the two residents' associations in December, saying that: "Tenant-led transfers fit well with the government's localism and big society agendas… Transfer can empower local tenants and encourage people to take an active role in their communities."

The department is preparing to implement powers inserted by the last government into the 1985 Housing Act – as section 34a – that would require local authorities to co-operate with residents' groups wishing to change the ownership of their estates to a registered social landlord, including one that they themselves control. To this end the campaigners have formed a company – West Ken and Gibbs Green Community Homes – and will start recruiting residents immediately, in readiness for taking advantage of the new rights when they come into effect.

At its own request, the government has been provided with two academic studies of quality of life in Walterton and Elgin Community Homes (WECH), a pair of well-established tenant-owned ex-council estates in nearby Westminster. Both studies appear to show that WECH residents are happier with a highly localist mutual as their landlord than they were under local authority control.

WECH took over running the estates in 1992 under Tory "tenants' choice" legislation, since repealed, in defiance of Westminster's controversial Conservative leader of the time, Dame Shirley Porter.

One of the studies, by Brighton University, concluded that WECH's style of housing management was "more effective at supporting individuals, instilling citizenship and building community".

The other study, conducted by the University of Stirling, compared the Brighton findings with national data about tenant wellbeing and found that the benefits of community self-ownership "appear to mitigate the detriment to wellbeing caused by financial deprivation, physical illness and fear of crime".

These results are backed up by residents Henley and Wilhelmina Joseph, who moved from a Westminster to a WECH home in 1996 after Henley had a heart attack. "I would say WECH nursed me better," Henley says. He praises WECH for its "reasonable" rents, efficient dealing with repairs and cultivation of togetherness.

The West Kensington and Gibbs Green campaigners look to WECH as a model they could emulate, although one, Ali Hashem, says there would be no need to if their council looked after them instead of, as he sees it, denigrating the estates as failures: "It's all on paper for them. But we live here."

Hammersmith and Fulham, however, defends its approach. A spokesman says it has a duty to explore whether what could be one of the largest developments London has seen for many years could benefit residents. He insists that residents have been given "detailed assurances that if their estates are included they will be offered a suitable new home in any development and that friends would be moved together".

A big factor in deciding which side prevails may be timing. Capital & Counties will be exhibiting its draft masterplan later this month. It may be significant that the developers have recently recognised that the new transfer rights could render the council "unable to secure vacant possession of its land interests".

Part of the campaigners' argument is that the estates are, as Taylor puts it, "already what the council says it wants us to be". She argues that a "mixed community" exists there already, a blend of leaseholders and tenants and people in a range of jobs as well as none.

Another West Kensington resident, Shirley Wiggens, says: "A community is made up of all types and you support each other. If there's a boy who I see swearing, I can say to him 'go and wash your mouth out'. It's because you've known people for years. The council just wants the money. We are just the peasants on their land."