Unemployed people will have to prove they are actively volunteering in the community in order to qualify for certain welfare benefits and social housing under "civic contract" proposals drawn up by a Conservative local authority.

In measures aimed at ending what it calls the "something for nothing culture", Westminster city council also proposes that working families who "play by the rules" should get priority for social housing, while existing tenants who fall foul of the law should be evicted.

The central London council says it wants to draw up rules governing residents' entitlements to locally controlled benefit payments, social housing and public services to ensure that decisions about how to deploy shrinking welfare resources are guided by the principles of "responsibility, fairness and opportunity".

It claims its proposals, set out in a consultation document published on Monday, are a potential model for the future of local public services across Britain. It says: "A culture of 'something for nothing' is no longer financially possible and is not the kind of society we wish to foster."

Other measures outlined by Westminster council include a £1-a-night tourist levy on visitors staying in hotels, the imposition of full council tax rates on its 9,000 second homeowners and increased charges for a range of council services.

But the proposals around benefits and housing – including the claim that social housing is "a privilege, not a right" – are likely to cause most controversy.

The proposals include:

• Means-testing social housing tenants so that households earning above average local incomes will pay higher rents.

• Giving priority access to borough's 22,000 social homes to groups such as volunteer police officers, Territorial Army members, nurses and ex-service personnel.

• Giving social housing allocation credit points to families who adopt or foster children; and deducting points from housing applicants found guilty of antisocial behaviour or families whose children persistently truant from school.

• Reducing council tax benefit for households whose members are convicted of persistent antisocial behaviour or criminality.

Westminster's consultation also asks whether it "should expect benefit claimants to do more community-based work to help other residents whilst they are in receipt of benefits".

People applying for social housing should be able to build up additional allocation points by volunteering, it adds.

Westminster's Labour group leader, Paul Dimoldenberg, said: "This is not about the 'big society' but about Conservative 'two nations', where the 'deserving poor' are tolerated so long as they do not cause any problems or cost too much.

"The Conservatives see the best way of cutting the cost of local services as moving poorer families out of Westminster and thereby reducing the cost of education, social services and other public services."

The council's own estimates show that up to 5,000 of the borough's poorest families currently living in private rented accommodation will be forced to move when government-imposed housing benefit caps take effect next month.

Westminster's civic contract proposals amount to the most striking example yet of Conservative attempts to cope with huge budget cuts by refashioning local government along "big society" lines and introducing conditions into welfare provision using powers granted to them under the Localism Act.

A series of big society-style "urban citizenship" proposals outlined in the document would give residents and local businesses the power to take over the running and management of public parks, libraries and streets, to create "strong unified neighbourhoods where civic responsibility prevails".

The council leader, Colin Barrow, said: "Asking everyone from businesses, residents and the wider community to play their part – no matter how small – is important in changing people's expectations away from a culture of getting something for nothing."

Other proposals draw on the "nudge" approach to changing social behaviours, such as removing refuse bins from streets in residential areas to encourage recycling.

But the council, which is planning a crackdown on youth gangs in the area, also says it will not hesitate to take enforcement action against people "that break the rules and cause inconvenience or unpleasantness to others".

Westminster includes the Houses of Parliament, Oxford street, and Soho's bars, restaurants and theatres. Nine out of every 10 visitors to London pass through Westminster, the council estimates.

It also presides over some of the most extreme inequalities of wealth and health. Life expectancy for the millionaire denizens of Mayfair and Knightsbridge in the south of the borough is typically 13.5 years longer than that of residents of the council housing estates in Queen's park in the north.

Westminster's civic contract consultation runs until February 2012.