A growing number of councils are asking wealthier households to pay a voluntary “mansion tax”, with one local authority leader calling for similar schemes to be rolled out across the country.

Surrey and Kensington and Chelsea local authorities are both preparing to follow the example of Westminster City Council, which has raised £900,000 from households in the highest council tax band making voluntary contributions on top of their usual bill.

The disclosure comes after a major row over plans that have been considered by Downing Street and the Treasury for a possible new tax on owners of expensive properties. Last week The Sunday Telegraph revealed that Boris Johnson had effectively shelved the idea following a backlash among Conservative MPs and grassroots.

Rachael Robathan, the Conservative leader of Westminster City Council, called for other local authorities to follow Westminster’s lead in asking wealthier households to make voluntary contributions on top of their council tax bills in order to increase funding for local services.

She said: “When we proposed the idea of a voluntary community contribution two years ago, some people were cynical and said our more affluent residents wouldn't be prepared to pay extra to help those less fortunate than themselves.

“The fact we have raised more than £900,000 so far is proof that what started life as an untested experiment is gaining ground. This money is also being returned to our streets in the form of grants to tackle loneliness, rough sleeping and to support our young people.”

She added: “It would be good if this kind of voluntary community contribution system could be rolled out across the country. If it were adopted more widely, our experience suggests it could bring in extra revenue for councils they currently can’t access.” Ultimately, however, Ms Robathan favours adding additional bands to the higher end of the current bandings used to determine how much council tax each household pays.

This month Tim Oliver, the Conservative leader of Surrey county council told councillors that he had held talks with the local authority's chief executive about "invit[ing] residents to make voluntary additional contributions to council tax." Band H households in the country are due to pay £3,022 in tax to the local authority this year.

He said: “There is nothing to stop this council asking people to make more contribution to council tax if they so wish and I’m sure there are some residents who would be happy to do that.”

Kensington and Chelsea council is setting up a charity to manage a "voluntary contribution scheme" after a survey of 1,172 Band H households found that 67 per cent supported the scheme and 61 per cent said they would contribute.