I moved to the UK (not from the US, but from Europe).
If you're going to live there you'll need something that will work on the long term, so you'll need to find yourself a gp that is okay with prescribing your hormones. In order to find one that is willing, you'll need a statement from your current gp that you're diagnosed and such, prescribed T and under monitoring. If you're not monitored anymore, then your UK gp may want you to find monitoring in the UK. At least, mine did (but I was lucky enough to still be monitored through the genderhospital in my own country).
I had no issues finding gp's to help me out, but only because I had those statements. If you don't have them, try to get them before you move. It may be difficult to get help without them. The genderteams in the UK are overcrowded with 2 year waiting lists, so don't expect help from them anytime soon.