I haven't done it yet, but I'm in the same situation. We don't have enough money saved up to support ourselves indefinitely while job searching, so we can't move over until I have a job offer. I'm a UK citizen, so I can job search freely ahead of time. My gf won't be able to until she has her visa.
What I plan to do is pick a moving date, and in my cover letters state that I will be living in London as of that date. I hope that level of certainty will help. (They don't need to know that I won't move if I don't get a job--if they don't hire me, what I do is of no concern to them.)