I would second Jas' advice not to make the mistake of living anywhere too expensive in London, cos as long as you keep costs down and charge an average rate (or more
) there's no reason this city should be too much of a challenge if you've already worked really successfully elsewhere!
Travel and eating out can be pricey but you can also be quite frugal if you want/need. For exame, you can go out as much as you like as long as you don't 'need' lots of drinks to sustain you; have a glass of wine before you leave, and then maybe only one or two at the pub/club/restaurant/etc! And it's a good idea to avoid living on your own - sharing with one or two others reduces the cost dramatically (if you want to be within Zone 2 - further out is more affordable so a one-bed place can be more feasible).
I'm a student and I've recently limited my working days to 2(!) with the somewhat surprising result of having a small queue of interested clients wanting to see me on those days, and leaving me free to focus on my bloody endless assignments the other 5 days of the week! Well, 4... cos I take at least one day completely off, too.
London is absolutely packed full of prossies and clients, so no point sitting about worrying about the competition (I'd pull my own hair out in panic if I spent my days browsing through all the supermodel-ish profiles!) because all you need to do is set about establishing your unique identity as much as you can. Blog/Twitter/etc help, but mostly just market yourself with confidence cos tons of guys will want to meet you.