So I'm an American also living in the UK! (though in Scotland) but I've been cosplaying across Scotland, England, and Ireland for about two years now. No one cares that you're American. People don't even ask that much when they hear your accent, and I've been confused for just faking it for my character, so don't be worrying about that, heh.
Best conventions I have been to while I have been here are London MCM Expo, which happens twice a year, Sunnycon, which is a newer con in Sunderland in the spring, and Q-Con, which is in Belfast every year and will be in its 20th year next summer.
I've heard great things about Nemacon in Newcastle and Nomcom in Dublin as well, so I'm hoping to attend them sometime soon.
As for arriving, I've always put on my cosplay in my hotel or wherever I am staying and travelled in cosplay. In London, NO ONE bothers you or even looks twice, and that includes on the London Underground. The closer you get to Expo, the more cosplayers you run into anyway, but seriously. I mean, I was dressed as Jin Kisaragi from BlazBlue last fall, about 45 minutes away from Expo still and someone random on the street asked me for directions. Me. Out of everyone around me. So yeah, don't be worrying about that.
Otherwise, be ready to understand that British cons are different as far as programming goes, and tend to be smaller, but they're still a lot of fun and have some amazing people at them!^^ And some great cosplay.