I've seen a few posts asking how to go about Marrying a UK citizen or marrying a US citizen, but I cant seem to find one about marrying in the US and then staying in Britain.
Can anyone steer me in the right direction?
A non-US citizen can get married in the US without a visa (ESTA is fine) as long as they don't intend to immigrate. Check your state/local requirements here: https://www.usmarriagelaws.com/ (you should also call the town/city clerk to see what ID requirements they have)
After marriage, the American spouse needs to apply for a UK spouse visa from the US. It takes about 1-3 months on average. The British spouse needs to be earning at least £18,600 with the same employer for 6+ months, but there are other provisions (and combinations of which) if the situation isn't so straightforward.