No, you do not have to do the "whole shooting match" again. However, you do have to do all the theory and sit all the exams, and that's the major hassle.
Once you've done that, you need a minimum of 15 hours flying training to convert to a JAR IR. Your license will state that the IR was a conversion from a foreign IR, and other JAR countries are not obliged to accept it (whereas they would be obliged to accept a "genuine" UK IR) although I've not heard any storied about anyone not accepting conversions.
FFF
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[Edit] Or, if you're only going to fly your G-reg aircraft in the UK and you don't mind staying off the airways, you can get a "free" IMC rating once you've got your FAA IR. Just send your license to the CAA along with the correct paperwork and a cheque, and they'll add the IMC rating to your JAR PPL without any further training.