So you are offering to give the insurance company £2 - £20 to up your insurance so they can pay out £2k - £2.5k?
We had an incident a few years ago at an airbase i was working at, a trainer hawk aircraft crash landed, slid into the Air Traffic Control Tower damaging the staffs cars parked in the car park. There was a right performance when staff came to claim and it all depended who you were insured with as to whether you were covered. Some refused due to no commuting insurance and some even refused payout because they did not have specialist airfield insurance - wtf is that?!
I appreciate your personal situation, but the b&w is that you do not have Social and Commuting. Insurance companies would rather not pay out and you have just handed them the golden ticket. The only thing you can rely on is their goodwill:
https://www.confused.com/car-insurance/guides/car-insurance-classes-of-use
Wouldn't they claim from the negligent party? Ie the party responsible for the aircraft