A potentially slight amendment to STP's posting...if the FAA licence that you mention is issued on the strength of your UK licence...EITHER an FAA or CAA medical is sufficient to validate it...you do not need both.
If the FAA licence was issued as the result of an FAA course of training and FAA flight test - you do need both..though, if the latter is true, your CAA licence and medical would be of no consequence - so, again, you wouldn't need two medicals.
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