Just to let you know, I'm not an expert, just a layperson who's researched immigration semi-extensively, hehe...
Your best bet would probably be the US K-1 fiance visa since you'd like to both marry and live in the US- it's the most straightforward route for your situation. Basically what happens is that your fiancee files a petition with American immigration to establish that you're a genuine fiance, and when it's approved your case gets sent to the US Embassy in London to apply for the K-1 Visa. After a medical exam and an interview in London, (hopefully) your case is approved and you now have 6 months to enter the US with your K-1. After you arrive in the US, you have three months to get married, and after marriage you file for adjustment of status to a US Permanent Resident. While you're waiting for that to be approved, you can get temporary employment authorization so you can work as well as a travel document that allows you to leave the country (since the K-1 is single entry, if you leave without getting that travel document, you have to start the visa process all over again.) After your adjustment of status application is approved, you become a permanent resident of the US and get a "conditional" green card (since you'll probably have been married less than 2 years at that point.) After the two years of your conditional permanent residence is up, you must apply to remove the conditions on your GC and get a regular GC that expires every 10 years.
It's a lengthy, expensive process, but if it's the best option for you, go for it- people from the UK in general have an easier time of it than many other countries. The best place on the Internet to get info and advice on K-1's and other marriage based visas is
http://www.visajourney.com- that should be your first stop. From what I've seen on VJ, the average time to get a K-1 from the UK is maybe about 5-6 months or so...depends on where your fiancee lives (which affects which office she files with.)
I don't know anything about work visas, but seeing the almost draconian US immigration process for marriage leads me to believe that a work visa is probably very very hard to get without specific qualifications. That's also the case in getting a work visa to the UK, unfortunately.
Now, I gave you the most straightforward route. If you want the absolute fastest route to being together, and your fiancee is willing to move for a little while, you can marry in the US (perfectly fine to do that as a visitor if you're planning on going home afterwards!) and then get her a spouse visa to the UK- you can get that on the same day if you apply in person, or in a week or two if you apply by post. Then you'd get to live together in the UK while you file an application for a spouse visa in the US and wait on that to be granted. But from the info you've given, I'd say go with the K-1
Hope this helps!
