Hi,
You'll need to search out specialist insurance brokers and providers and have them look for specific policies and/or underwriters.
It is possible to have insurance here in the UK if you are not a resident here. 'Generally' speaking, you'll find it's the very/super wealthy who'll do this kind of thing, I've met a few people who bring their cars in from the USA and Dubai/Bahrain for a few months of the year and then take them back. Substitute of course that you'd be wanting to register and keep a UK spec vehicle here.
A quick search shows;
https://www.keithmichaels.co.uk/specialist-car-insurance/expat-car-insurance/living-abroad-with-a-uk-car/https://www.moneymaxim.co.uk/short-term-car-insurance-uk-overseas-residentshttps://www.temporarycarinsurance.ws/driving-guide-for-foreign-visitors.htmlWhen you aren't in the country, then as it's most likely you'll get a temporary insurance policy, I'm 'speculating' that you'd need to store the car off road, declare it SORN with the DVLA so that you won't have to keep paying the VED fee/get a refund for the months it's valid for but you don't use due to going back to the US and the car being SORN (statutory off road notice)
Depending on how deep your pockets are, what kind of car you want, then that'll affect how much you'll pay whilst you're not in the UK. If you do have deep pockets, then do what those guys I mention above do! if your pockets aren't so deep, then I'd also suggest renting each time you visit. The guys above would bring their Ferrari's Lamborghini's and other exotica over and the relative high cost of insurance would be like loose change in their pockets.
I'm within the Automotive sector now for manufacturing and electronics, so have a pretty extensive network amongst all sorts of sub sectors. There's one specific resource to get more information I know of, but by the very nature of your question.. the guys I want to talk to aren't in the UK right now!!!
Disclaimer - I'm also assuming that as a non resident, DVLA will allow you to register a car in your name even if you don't have a UK address. Speak to the DVLA and the insurance specialists above to find out more. I 'suspect' that it might be that these temporary policies will be for a car you bring in temporarily. It 'might' turn out to be it's insurance you can get where your friend is down as the 'Registered Keepr' but you are the 'owner'.
http://www.dvla-contact-number.co.uk/the-differences-between-the-registered-keeper-and-owner-of-a-vehicle/Plenty of research for you to do! Please report back with how it pans out as it'll be useful to other's thinking of doing the same.
Cheers, DtM! West London & Slough UK!