As
@vickster says
Whereabouts in London are you and how far are you prepared to travel?
A while ago I got a bike fit from Denver Collins at Panagua bikes (I don't know if he's still there) and it was an interesting and, I thought, useful experience. But they are a bit out in the sticks at Hayes (Kent)
https://panaguabikes.com/
Did it help with "performance". I'd say "yes, but". Performance for me is about being able to ride all day (or sometimes all night, and very occasionally both) in comfort - or at least delaying the onset of discomfort. Some of the things Denver did definitely resulted in the bike being a tad more comfortable enabling me to push my distances a bit further. Didn't make me any quicker though. I'm beyond help in that respect.
Many people are - probably with good reason - sceptical about the value/benefit of bike fits. You can certainly get it "good enough" yourself - and it would probably be a good idea to do this and ride it a bit to get a feel for the bike before going for a bike fit. People here will be happy to give you lots of clear* advice.
*Sorry, I meant "contradictory and confusing"