A voluntary 'mansion tax' on properties worth more than £10m is being considered by Westminster City Council.
The council is to consult residents in 'super prime' properties on introducing a new council tax supplement of £1,376 per property.
This would raise £2.75m in revenue for the council and would enable it to freeze council tax for all other bands.
Leader of Westminster City Council, cllr Nickie Aiken said: 'Westminster is home to some of the poorest and richest people in the country and some of the most expensive real estate in the world. But while there is a reality to the cost of living in a capital, this is a council and a Government committed to fairness. There is more we can do to help those who are struggling to pay the bills.
'One way of doing that is via a voluntary supplement linked to the top council tax band. There is no appetite from central Government to revaluate council tax, but we believe we have come up with a method which will allow the well-off to voluntarily help those just about managing.'
The council is also lobbying the Government for new legislation so it can make the new council tax band mandatory.
