Look at the Fingerprinting Process FAQ on the TSA website, questions 7&8.
https://www.flightschoolcandidates.g...§ion=FQ#F7
This directs you to the CTC webpage, where I found the following UK locations where you can get fingerprinted:
TSC
FlightSafety International UK Ltd - Farnborough, Hampshire, United Kingdom
Oxford Aviation Training - Oxfordshire, United Kingdom
So yes, it looks like a trek to Farnborough is possible.
OTOH if you simply resubmit your application in due time, won't that be cheaper?
Oh, and about AFSP personell who can't even read their own FAQ...