Rachel, I know you PMd me about working as a graphic designer here in the UK. I hate to rain on your parade even more, but prepare yourself for a hard time. The design industry in this country is very insular and very competitive. I can virtually guarantee you that no employer will hire you over the hundreds of qualified British and EU candidates who will apply for their vacancies. Unless you are the next Paul Rand or Paula Scher, they have absolutely no need to attempt to hire an American when it's so much easier to hire an equally qualified British or EU citizen. I know you said you've had some initial good responses, but that is typical British politeness and by no means guarantees any follow-up. And unless you tell them, many design firms may not even be aware of what is required to try to hire you so you could get an offer only to have them back out once they realize what the work permit process is - even if you are willing to pay for it.
Proving they have advertised the position and that no British or EU candidate is qualified is the real sticking point. Everyone thinks they are a designer these days.
Now I'm not saying it's impossible to find a job. And if you are in Birmingham, you've probably got a better chance than I do in the semi-rural south west. Despite my 8 years of experience, I also found that no one was particularly willing to consider me for Art Director roles as they didn't want to risk having a loud obnoxious American in a position of authority. Yes, I was really told that! (OK, not those exact words, but that's exactly what they meant!).
Here's a little example of how tough the design/journalism/media/advertising can be if you aren't already legal to work here. A friend of mine did a semester abroad in Manchester back in the early 1990s. Part of her program was interning with the BBC. They liked her so much, the wanted to hire her for a summer job. But even the BBC couldn't get past all requirements - even for a short term position. And things are much more stringent now than they were in the early 90s.
So your best bet, whether you want to hear this or not, is as Lola said, get married in the US or come over here on a fiancee visa. But I'm not sure you could get either of those by mid-August.
Good luck!