They have a motor policy, suitable for them as a business, in the same way that a motor trader does or when you borrow a bike for a test ride. Their premiums will, presumably, not be the £100 for a year that you read about on these pages but that doesn’t matter as they they can pass the cost on to their customers.
I am sure that it’s not the foreign licence that is the main problem, not least as lots of bods living in London on a temporary basis (but long enough to have a permanent address) buy UK motor insurance without too much problem. The problem comes in that most run-of-the-mill insurance providers are only set up to deal with simple tickbox customers, British licences on a British registered bike with a permanent UK address. There is no real demand for them to do anything but.
If you do hit on a solution, let the forum know, as I don’t recall it ever being answered successfully. One company you might try to approach is Equity Red Star, who, as a Lloyd’s syndicate might be more flexible. That’s just a wild guess though. Similarly, Axa, used to be quite helpful, I think out of an office in Milton Keynes.