Hey there ....I'm in your same boat!!
.....And it isn't an easy boat to be in. I found this out quickly when I thought that I could just pack up and go. Oh no no no , unfortunately. (unless you are very wealthy)
School of course is the easiest route. Other then that it's very hard to get a work visa being an American. British companies have to post the job for at least 6 months and if they can't find a Brit to fill it then they can look elsewhere.
If you have British ancestry, you can get over there that way. There is also a fiance visa , but you can't work while over there on and you have to have a wedding set for 6 months down the road.
You can also try the highly skilled Migrant program, there is a calculator to see if you are eligible at
www.workpermit.comI am doing a lateral transfer with the company that I am working for now in New York. I am very lucky for this, but it is not as easy as I thought. I am pretty much indebted to my company and if I leave them once I am over there then I have to come back to the US or find another company to sponsor a VISA for me!!
Good luck with everything and keep us updated. It is a long journey but I am sure that the outcome of being with your sweetie makes up for that