How to get UK Car insurance as an expat
 

Hope this is permitted - I thought it might be useful information for anyone in a similar situation to myself. I am a UK non-resident expat but have a UK car. It's been incredibly difficult to insure but I have finally found a few insurers willing to do it provided you have a (genuine) UK address you can use where you stay at least occasionally during the year. I mention the actual price I was quoted as well in case that helps others in future.

Aviva - (they quoted me £480 - so I went with them)
Keith Michaels (they quoted me £850)
Admiral said I could be a secondary driver if I could get someone who is a UK resident willing to be the primary driver - but obviously don't lie about this as you'll get in massive trouble if caught. I didn't want to go this route so didn't get a quote.

Companies that turned me down flat include: AXA, Debenhams, City Insurance and I tried all the online insurance comparison sites (such as moneysupermarket or gocompare) but they all hit you at the last second with an assumption that you are UK resident which you cannot turn off so it was a massive waste of time.

I had to call by phone (online didn't work as they make incorrect assumptions which you cannot change) and in all cases I had to be persistent as the initial response was "we can't cover you" and it was only when I persuaded them to check with someone more senior that it was OK'd (apart from Keith Michaels who said straight away it was OK).

Do also stress very clearly that you do not live in the UK and do not have a current UK driving licence but you do hold a valid licence from the country you're living in in order that there is no confusion. It seemed to help that I had a UK licence from before I left the UK but make sure you clearly say that this is not the licence you will be driving on.

Do record the call and screenshot / save every page of the website and anything they send you by email/post for your protection just in case they come back and claim you didn't mention expat non-resident status or some other nonsense down the road.

Good luck!