How easy is it to keep an FAA IR valid in the UK?
As easy as it in the US, though doubtless somewhat more expensive. Here is a user friendly guide, you can find the FARs on the faa.gov web site. Just complete the requirements and log it. No need to do it in US airspace or in an N reg plane.
IFR Currency Requirements
Every six months you need to perform at least six instrument approaches, holding procedures, and intercepting and tracking courses through the use of navigation systems. Failing that, you have, as was the case with the old regs, another six months to get current before having to take an instrument proficiency check. During that six months you may not file IFR.