What's the quickest Schengen consulate to issue a Visa in London?
Basically I want to travel as fast as possible to France, and since any Schengen visa will work, I want to go to the consulate with the shortest processing time.
As explained in Applying for a Schengen visa in another country than my main destination and elsewhere, you should in principle apply to the country that will be your main destination. There are a few other rules and procedures but in any case, you cannot simply chose a consulate that suits you, there should only be one competent consulate for a given situation.
If you apply to another consulate, you might get lucky but in all likelihood it will refuse to consider your application (as it should). In principle, consulates should do that quickly and then give you back the visa fees and all the documents you submitted so it's not as bad as a refusal but it would nonetheless cost you a few days.
If you are in a hurry, it's therefore especially important to apply to the right consulate from the get go (in your case the French consulate for your place of residence – not even another French consulate) and not waste time shopping around.