I know this isn't the answer you are looking for but...
You would be crazy to attempt to park for free in central London.
First there is the congestion charge. This means it is going to cost you eleven pounds to simply bring your car into London, even if you park for free.
Second, while there is free parking in London (but very little), what there is always has very tight restrictions and is incredibly popular. Even if you found free parking, your chances of being able to park there are negligible. 'Unrestricted' free parking, that allows you to park all day for free, would be taken by about 12.02am.
Third, driving in Central London is extremely crowded and not that easy. Unless you have a really good reason, or enjoy being yelled at by other drivers, you should reduce your stress levels and stay out.
Fourth, almost everybody who visits central London wants to move around, and by far the best way to do this is use the underground (or the bus, but mostly underground). If you are going to do that, you may as well park outside the centre and get the underground in.
Finally you are going to say "what about the locals, what secrets do they have about parking in central London?" Well, the locals do have a secret, and the secret is - they use the underground. Even if you live in central London, most people use the underground to get everywhere.
If you absolutely have to bring a car into London because you or a passenger are disabled and can't use public transport, that's an entirely different matter.