Title 14 Chapter1 Part 61.3
blablabla...However when an aircraft is operated within a foreign country with a current pilot certificate issued by that country, evidence of current medical qualification for that certificate, issued by that country, may be used. blablabla..
TITLE 14 Chapter1 61.3 4. Airman competency;
blablabal...at the same time, provision is made to allow the use of a current pilot certificate issued by the foreign country within which the aircraft is operated.
These rules are not new they are the current Docket since june 1966...
N register airplane in UK... Uk licence current + UK medical OK ; FAA licence Current + FAA medical OK ; FAA licence + UK medical OK. BUT :
you cannot mix the ratings ie FAA MEL IFR , UK SEP VFR; you cannot fly a N registered single Engine IFR.....
The easiest is to keep current on the airplane you seek to fly ( licence wise); regarding insurances, many times it states something like ' necessary for operations with x hours PIC on class/type/ etc..."
Have fun ! and remember : stay out of the trees !