I think some of the earlier replies are incorrect although I have no authority to refer you to. My understanding is that your FAA license is valid all the time your UK license is valid. Valid does not mean your UK medical or proficiency check has to be valid, simply that your UK license is valid. Of course an old style license is for life but the new license requires renewal every two years I think. That seems to me to make sense because for your FAA license to be valid so must your FAA biennial and your medical. You cannot rely on your UK proficiency check not least because the aspects covered in each of these checks are different. For example power on stalls are not usually included in the UK proficiency check but are very much a part of your FAA biennial. Interestingly there are some examiners in the UK who will cover both the UK proficiency check and FAA biennial in the same hour, and then sign of both.
I suggest you take a look at the FARs for a definitive understanding.