Andrew Lloyd Webber told the Evening Standard he was “stunned” by the proposals, which it is predicted will have a damaging effect on businesses across Theatreland.
"In our industry alone, the benefit in terms of revenue to the council will be exceeded many times over by loss of sales, not to mention the inconvenience to families of Londoners who look to weekend parking to enjoy theatre, one of the city's greatest assets," Lloyd Webber said.
From 9 January, the council wants to abolish free parking on single yellow lines between 6.30pm and midnight Monday to Saturday, and between 1pm and 6pm on Sundays. If the plan goes ahead, it will see motorists being charged up to £4.80 per hour to park in Soho, Covent Garden and Mayfair.
The plan, dubbed by commentators as a 'tax on nightlife', is just one of a number being rolled out by councils across the country.
For the West End, which is already anticipating a considerable fall-off in business during next summer's Olympic Games, the effect could be particularly damaging.
Mamma Mia! star Sally Ann Triplett told the Standard: "Actors already work unsocial hours and why should we be penalised because that's the job we do? Mostly we adore our jobs but actors don't get the best wages in the world. People can live up to two hours away and they need the flexibility to be able to use their car."
Fellow actors Actors Tom Conti, Linda Bellingham, Bill Paterson and Roger Lloyd Pack were among those who signed a petition against the plans, which was submitted to the council earlier this month.
Other critics of the scheme include London Mayor Boris Johnson and president of the Society of London Theatre Mark Rubinstein, who said the proposed abolition of free parking has come at "entirely the wrong time".