The issue actually isn't usually who can carry out maintenance, but who can certify it. Usually there's no problem with an M3 organisation doing the maintenance, but you might need to counter-certify the maintenance yourself, or get a PFA/BMAA inspector to do so for you if they haven't one on the staff.
Seriously however, you can't afford to totally relinquish all responsibility for a permit aircraft - you need to take an active interest in what's being done, check the tech records, confirm that the right inspection / maintenance intervals are being adhered to, MPDs (Mandatory Permit Directives - like ADs) complied with, etc.. You can't rely upon it all magically being picked up by a LAME and CAA procedures in the way many CofA aeroplane owners do.
G