It's possible, and I'd agree that it's well worth doing the exams before heading out to Florida - doing a three week PPL will be fairly hard work without the added effort of studying for seven exams in the evenings.
One of your local flying schools should be able to help with the writtens (you don't say where you are in the UK). It isn't unknown for people to get a bit grumpy when they hear that you're off for cheap flying overseas, so a bit of tact is probably worthwhile (but if so then I might suggest that's possibly not somewhere you would want to fly once you're back...
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