When I obtained my FAA Temporary Airman Certificate to fly under PPL privileges in the US (not that I've ever actually done so), the FAA chap picked up the US certificate in one hand and the UK licence in the other. "This", he said, waving the US certificate "is only valid if this UK licence is kept valid".
So I would say that if your FAA licence is a Temporary Airman Certificate, then no - as your UK SEP Class Rating has now become invalid, you will need to renew it by flying a SEP renewal proficiency check with a UK Flight Examiner before it can be revalidated. The flight is quite straightforward, you will need to fill out a LPC-SPA form as well but (assuming you pass the check) your licence will be valid as soon as the FE signs it - and you will not have to send any cheque to the CAA either!
However, if you have a full FAA PPL, you should be OK to fly on that as you've flown a BFR. I'm not sure why you bothered with a BFR if you held a Temporary Airman Certificate - the FAA told me that a BFR is NOT needed if your UK licence is kept valid.....
Last edited by BEagle; 2nd Apr 2002 at 06:39.