Here's a word of advice from someone who's been there: it actually isn't much harder because you're an American. The only thing extra my companies had to do was check my passport & make copies of the visa to have on file, so they knew I had right to work in the UK. Everyone is used to foreign workers that it's not a big deal, and will almost never keep you from getting a job.
Waitressing isn't bad, actually. It has the added perk of a decent hourly wage (as in, about equal with what you'd make anywhere else in an unskilled job), plus tips. Tipping might be much smaller, but those little bits still add up. I made more when I waitressed in the UK than when I switched to a normal job with no tips (because I got paid the same hourly at both, see). It's not as 'quick' as in the US, but I still walked away every week with enough cash to pay my rent - I used my paycheck money to pay for other things. If you ARE going to waitress, make sure you do it at a place that does NOT have an auto "service charge" on every tab. Ours did & it was a rip-off, since the employees saw nothing of it & people used it as an excuse not to tip. I made enough to pay rent there, but at any other place, I probably would've made more.
That said, go for the normal low-end part-time jobs: retail, food, serving. Other Americans I knew got a job at Gap, for example. It's just like the US. You have to look around, have a good CV to submit, and be patient. Pubs are also good places to apply, but you won't make tips.
