If moving/relocation weren’t stressful enough, throwing in the element of an overseas move makes it a very difficult time.
It’s a common misconception that an American can just pick up and move to the UK just because they’d like to. This is entirely untrue, you need to qualify for a visa to move to the UK!
UK Immigration can be pretty cut and dried, that is, simple and to the point, you may well not need a lawyer, you usually can do the paperwork yourself (for straightforward fiance and spousal visas anyway). There are several different ways of emigrating to the UK, and finding the right one for you can get complex, so make sure you do all your research before you buy your ticket!
The main ways that US nationals come to the UK are as visitors, as fiancee’s/spouses/civil partners of UK or EEA nationals, or tied to studies, employment or investment. With all of these categories, it is essential to prove that you will not need to be supported by state funds (ie welfare) once you get here, and that you have somewhere to live.
It is important to note that not just *any* job can get you a work permit, and a casual relationship (ie one where you have not been living together and do not yet intend to marry) will not give you enough ties to emigrate.
The pages here give some detail on the different categories, and give links to government departments which contain the information you will need.
More about Visas, Immigration, and the IND (Immigration and Nationality Directorate)