What's your visa situation? I'm not 100% sure but I don't think there's a Working
Holiday visa for the UK open to USA residents, just Commonwealth citizens. I could be wrong though! If you can't get that or an Ancestry visa, then it's tricky - to get a working visa, you have to have a guaranteed job and your employer has to be able to prove that they couldn't find anyone in the UK who was capable of doing the job - and with the number of technical graduates moving into the workforce every year, your chances of that are pretty slim.
Anyway, that aside, the best place to look for jobs is The
Stage, a weekly newspaper which also has a very good website -
clicky here!. If you're interested in working on the West End then your best bet is to go door-knocking and just ask for the chief electrician at the
stage door. I never did that myself (I spent two years working in the UK - being a Kiwi I was able to get a Working
Holiday visa) because I get bored with monotony and a West End show doing the same thing day in, day out would have driven me mad, but I know quite a few people who have got jobs that way. Sometimes West End jobs are advertised in The
Stage if they're slightly higher-level.