I married here while on a tourist visa and my daughter-in-law (she's South African) married when she had a work visa. We both soon after went to the British Embassy in our respective countries and applied for wife visas without any trouble. It's just that if your circumstances change, the next time you enter the UK (go out and come back) you have to apply first to upgrade your status (apply for the appropriate visa) before you come back in again.
However, my daughter-in-law had an additional saftey net I didn't have. With her work visa, she could still enter this country for another year...basically, she went to the British Embassy in Johannesburg to apply for her wife visa knowing full well that if she didn't get it, or if she'd forgotten some paper and had to re-apply, she could still re-enter England under her work visa for another year. She had her visa within an hour.
As for notifying the US Embassy, you'd probably do that when you want to change your name in the back of your passport. (It's also generally a good idea to let the Embassy know where you are in the UK...but it's not a case of them hunting you down, or you getting into trouble for not telling them.) I was able to do a number of things at the Embassy at the same time, like change my name on my Social Security, apply for voting absentee ballots...in other words, after your name changes, visit the US Embassy in London and just go around to all the offices there you need to. The IRS even has an office there.
As for not applying for a fiance visa...not a problem! You're merely skipping some paperwork and additional waiting.
