Its expensive too especially if your central - zone 1 etc your looking at £30-£40 a day not sure on overnight rates, if your staying at a hotel ask them whats best they might have better rates etc, or if at someone's house then park on the street most are free from 5.30/7pm till 8/9am so just make sure you move it before hand
Edit: mayfair is a bit different best check the signs, there is a car park at the holiday in on berkeley street and a pcp place just off park lane and another just off the square but they will not be cheap. You have guy ritchies pub and some nice restaurants, banarez if you like indian, hakasan for your asian and the square for your french stuff, plus a bentley, rolls royce and porcshe garage to peruse, Its a different world