Legally, if you have a JAR PPL, you will not need any conversion, you can just jump into an aircraft and go.
From a practical point of view, though, if you're renting an aircraft from a club, the club will require you to do some kind of checkout with an instructor, the same as every other pilot who wants to hire from them.
However, you should probably expect your checkout to last a little longer than the average pilot because your instructor will want to make sure you are up to speed with the differences between flying in the UK and flying in the US. The main differences will be the radio terminology, airspace layout and the good old British weather.
If you are lucky enough to own your own aircraft, then although there is no legal requirement for any kind of checkout, I would still recommend very strongly that you spend a couple of hours with an instructor anyway.
Hope that answers the question.
FFF
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