As far as I know pro firms in the sense that firms like Bright etc do not exist in London.
We do have day trading firms, but because UK stocks have 0.5% stamp duty, they trade USA stocks. So they trade between 2.30pm and 9.15pm, and provide "lunch" at 5pm!!! Really there is no cost/leverage advantage to trading privately from home though.
The other thing I was told (which really smacks of the nanny state we have here!) was that if I was going to get an exchange membership on, say, the cme - so I could trade globex at home for cheap fees on even my own account, I would also have to register with our own UK Financial Services Authority - an overtly expensive and burocratic process. Ridiculous, but then you also suffer with pathetic government rulings designed to save you from yourself! Liberal democracies - don't you just love 'em!