Are you planning on getting a full ATPL? Or just going to do leisure flying? Depending on the school in Florida I probably wouldn't reccomend it.
If you do choose to go there make sure you get a JAA school so you'll have the same license but I think when you are just starting out it is good to be familiar with the country you are flying in. The US has different radio (similar but alot more slack) different airspace, different circuit joining procedures, if you do an FAA PPL then the manoevers you do are completely different to what you'd learn in a JAA PPL.
I did 15hours in England flying (to solo) then did the same as what your thinking, went over to Florida and everything was just different to what I'd been learning and so I ended up cutting it short in FL and went back to England.
I'm flying in the US atm doing my CPL as Oxford send their students to Arizona and now I'm a more expierienced pilot the differences don't seem very big to me but when your first starting out they do well in my opinion anyway.
I've heard OBA are bad so avoid them! Get your PPL in England get more expierienced then go on a flying holiday over to Florida or something.