"Post Brexit has complicated matters for fractional ownership aircraft, with foreign and GB registrations, now unable to use unlicensed airfields."
Is hooey!
Your aircraft has or has not ('sounds like has) national authorization to use any aerodrome which is dimensionally suitable - but that's not an insurance thing. If you're a G reg plane in the UK, you can land anywhere for which you have permission from the landowner, and that should not concern the insurer. Now, if you try to tuck it into a too short grass strip, and wreck it off the end, the insurer may justifiably "inquire" about were you operating within the performance of the airplane, and that brings up other questions. But if you're operating off a runway of suitable condition and dimensions, and with permission, that should be the end of the insurance company's interest. I would press the issue with the insurance agent. I have known flying club airplanes, where it was the flying club policy that you not take their plane into unlicensed runways, that was a flying club policy, and fair enough, it's their plane. If it's your plane (or share of) and being operated properly, that should be the end of the concern.