I'm on the outskirts of London near Thorpe park, Heathrow etc. I work in central London every now and then but not shop fitting, I work on big posh houses. I did at one point work up there all the time for a big firm doing hardwood fixing fitting out offices etc. I got fed up with traveling on the train so stopped. I don't mind the odd job up there now and then and most jobs we do are my side of London in Mayfair.
I won't put you off as you need to do it to see what its like but you will find the wages almost the same as anywhere now where you used to get a premium for working in London. This is mainly due to all the cheap foreign labour that actually live in London
What ever you do good luck