The best flights would be from Gatwick to Orlando (either BA or Virgin, both direct) and do the springs to the north - about an 8/9 hour flight and the one i take home all the time. Or you can fly from Heathrow to Miami direct at least on BA, havent done the flight (as i dont need to) and have heard that Miami is a busy airport (not to mention city). From there you could explore the south east and keys within moderate driving distances. You can get other flights, but these are some of the direct ones i know of, you can take 12-16 hours to fly over including stops in all manner of hub airports if you really want to minimise cost.
Go into your travel agent (or online) and see what flights are available and prices etc, the diving is good in both these areas - the springs are one of the few places of really clear freshwater i have heard of. It also depends on your time constraints, you are probably luckly like most in the UK at having 4+ weeks vacation a year, we only have 2, maybe 3 if you are lucky - my mum kills me with 6 weeks vacation per year - i can only dream.
