It’s unusual to read a post where someone from the US wants to head over to this side of the pond! Usually its the other way round.
So as you are aware, as with most things related to working in a different country than what is on your passport - you will require a visa. Just doing a quick Google search it appears we have something called the Tier 5: Temporary Worker visa (http://tier5intern.com/)
This is news to me as from what I learnt from my international friends its pretty difficult to get a work visa in the UK these days after the rules changing in 2012. Hence a lot of them had to head home after they finished college as we also stopped our graduate visa (OPT/F1 status equivalent)
Internships in the UK aren’t like they are in the US. We usually call them ‘placements’ and they last around 12 months usually taken as a ‘sandwich’ during your degree. Our degrees are only three years so a student on some course would do a year in industry between their second and third years.
Some firms/studios will offer 3 months like the US but its down to that individual company. Hopefully your portfolio will be pretty strong given your US education which will be a benefit as you will be competing with a UK/EU student/grad for the same position who doesn’t need a visa.
You might want to check out TEAMS design who do a lot of medical work. Before you apply do your homework and don’t expect the firm to do the visa homework for you. Good luck!