Yes, countless threads here on this subject...
The cost differential UK v. USA is a lot less than it used to be. Renting in the UK has been in the region of £100/hour (plus instructor time) since I started flying 5-6 years ago, and back then you could rent the same spamcan over there for £30/hour, but when I was in Arizona earlier this year it was about double that.
Factor into that your time, the hassle with TSA and Visa issues (allow 2 months of paper pushing to get that lot done; email me if you need a step by step guide), food, accommodation.... even if you are young single unemployed and nobody loves you, the only thing which the USA has going for it is the good weather (in Arizona or S. California).
However, if you are a professional/business type, with a decent flying budget and you are doing this for real, to eventually buy a plane and go places, then you should be be looking at doing a standalone FAA PPL and IR, and you can't do an ab initio FAA PPL in the UK (can't fly here on the US Student Pilot Certificate, not to mention other issues). Then you are better off doing the lot, or the FAA PPL initially, in the USA.
For everybody else, you would achieve the same rapid learning if you pick a decent school and shack up next door to it in a B&B and live there for a few weeks, in the summer.