Well even though I live here, I don't know how you would move here, get visa's etc. I think if you do it as 2 year temp working visa you should be OK.
Anyway, about your original question.
London. Not the best place for 'speed shops'. What do you want to do? Actually be somewhere that builds race cars? Work in a shop that sells bolt-on bits, but don't know the first thing about racing itself?
Most the bolt-on shops, are mail order. So they can be based anywhere. Usually only poorly trained monkeys work there anyway.
Racing places. I know a few names, but there are so many places in the UK, and at all sorts of levels.
The MSA is the sports governing body. Their website is
www.msauk.org. There are some links there. However again not many places around London. Most are based near racetracks. There are the race teams themselves. Depending on the level, will depend on the qualifications and experience they want. Take it for granted that F1 teams, take the best engineers from Oxford and Cambridge Uni's. Mechanics are also experienced race mechanics.
Then there are component makers. DP Composites, SPA composites, AP Racing, Alcon and others that make parts.
Then there are small fabricators. Shops that do work for private club level racers.
Bear in mind living in London is mucho expensive. To start work somewhere, you may have to work for nothing or very little, not ideal for London!