There was a survey in one of Britain's quality newspapers that showed that London is the most expensive place to park in the world!!

With all due respect I don't think you will find free parking in central London except after 1.30 pm on single yellow lines on Sundays - or at least this applies to Chelsea. I would certainly consider a car to be a liability in central London - much better to use public transport. Might I suggest that you investigate Oyster Travel Cards or Day or 3 day Travel cards as a cheaper alternative to car hire, parking fees and regretably tow truck charges.