Your question implies you will be driving round London in a car in the week, which I would not advise, a car in London to get around to tourist sights is as much use as a chocolate teapot.
Yes there is free Sunday parking in a few places in that area, however IME these places get taken on Saturday evenings after 6pm (which is when the restrictions are eased), so if you are arriving on a Sunday morning they will be long gone unless you arrive really early, say before 9am. You could drive around for ages and might get lucky if someone just left one, or you might not.
You would be much better advised to use public transport on Sunday unless you are driving in from outside London in which case you'll just have to find a car park unless lady luck is in your favour. But if I was starting from somewhere else in central London in the first place, I wouldn't be starting with a car!