Hi Kelley, you're attempting to do roughly what I did "a few" years ago. Unfortunately, the visa laws and immigration restrictions have gotten quite a bit tougher since then, but the basic idea still ought to work.

I started applying for jobs (basically using job ads in the Sunday papers I could get in the US - but nowadays you can try the job ads in something like Monster.co.uk). In your cover letter, you need to say that you will be in their area "in the near future" and would like to discuss the job with them at that time. When you get a first nibble - i.e. any sort of positive response, asking precisely when you'll be over - you book yourself a two or three week vacation trip and over over to take the interview, and to follow up on any other job leads of interest while you're there.

If you succeed in getting any employer interested in you, they can help in getting that visa set up (though you'll have working permission only for that employer - if you lose your job, you have to go back home). You can improve your chances for finding a job if you have (or develop) some skill that is in short supply in the UK - you'll have to find out for yourself what that might be. In my case, it was being an experienced accountant with multiple languages.

The down side is that this approach can take quite a bit of time - and making one or two short-notice "holidays" over there to follow up on job leads costs a bit of money. Plan on spending at least a year (or even two) looking for that job - though sometimes things can happen faster.