It depends on how much money you want to spend. An undergrad degree in the UK will cost you between £7,000-8,000 per year just for tuition. Multiply that by 3 years and you're looking at a lot of money. Grad school can take as little as one year or as long as 4 or 5 depending on your course.
It's really up to you but if I was in your position, I'd do undergrad in the US, do an exchange programme to the UK and then come back for an MA.