Hi,

I just went through the same process - moving to London from New Zealand. I found that I had the most success when I directly applied to companies that I had a very very close fit with, rather than the more generic jobs. My feeling for more general jobs was that the companies weren't really interested in putting the time in if they couldn't meet me in person - but for jobs where I was a good fit they went out of their way to make it easy for me to interview.

I would recommend just picking a random company and putting some effort into an application for them, then rinse and repeat.