The council is expected to drop its objections to the proposal and seek a government grant for plans to allow pedestrians to walk freely in Trafalgar Square, Whitehall and Parliament Square.
The re-think by the council came after it was persuaded that the Government was serious about reducing traffic in cities by John Prescott's transport White Paper.
The Deputy Prime Minister has convinced the council that he is determined to go ahead with plans to tax business parking spaces in London and other parts of the country.
The council infuriated ministers when it blocked the pedestrian plans and demanded "effective traffic constraint" before approving the schemes.
There were claims that the Tory councillors had been "nobbled" by a Tory dominated local residents' committee, led by Tessa Keswick, an adviser to Kenneth Clarke when he was Chancellor.
Prominent Westminster residents include Alan Duncan, the Tory spokesman on health, and Virginia and Peter Bottomley, who have houses in the Smith Square area, which it was feared could become a "rat run" for drivers trying to circumvent the traffic closures.
The chairman of the council's planning committee, Alan Bradley, will announce today that the council is now ready to prepare engineering plans on the proposals, with a government grant.
The plans were drawn up by Sir Norman Foster and partners to allow pedestrians to avoid dodging the traffic in three of the most famous sites in Britain.
They would allow the partial pedestrianisation of the square by Westminster Abbey. Whitehall would be reduced in width from four lanes to two, enabling tourists to walk to the Cenotaph without dodging cars, buses and lorries.
The main feature would be the closure of the road to the north of Trafalgar Square, stopping the square from being used as a glorified round about, and linking the National Gallery to the pedestrian area for the first time. There would be bus-priority lanes, encouraging people to use buses or taxis when they want to travel from Westminster to the West End beyond Trafalgar Square.
Mr Prescott will go to Southwark today to support a scheme to limit city centres to "clean" vehicles which he launched in Chester at a meeting of European environment ministers earlier this year.
It will coincide with plans announced in Florence, Italy, to limit its traffic to clean-burn vehicles, or boats.Reuse content