I'm just going to reiterate what others here have said. It may be legal for you to come over as a visitor, look for work, then go back to the US while the work permit is applied for. However, I have been reading this board for a while and I get the distinct impression that work permits are very, very hard to get. In other words, you are more likely to reach the end of your 6 months with no job offer than you are to get one within your time frame.
So even though that approach might be technically legal, I don't think it's a good idea because it's not very likely to work. A fiancee or spouse visa would be a much better idea as you would not have the 6 mo deadline and you would be much more likely to get a job if you are able to work in UK already (which would not be the case on a fiancee visa but would be once you married and converted to the spouse visa).
It can take a long time to get a job after moving to the UK even with the legal right to take a job in the there! Just check out the jobs board. My brothers also moved over the to UK. They are both UK citizens, and they still had to do temp work through agencies for a good chunk of time before they got good permanent jobs (it was at least a year for both of them). This route (going through agencies) would not be available to you as a visitor. It would just make things much easier and would give you a much higher chance of success if you enter on a settlement visa.
