I started by trying to add myself to their existing insurance policy. After an hour of being shuffled around different departments, someone who knew their stuff told me that since Jan 2021 they no longer accept EU/EEA licence holders.
So I googled a few other companies who seem to specialize in non UK resident drivers, and again none are willing to accept me due to Brexit, pandemic blah blah. Just something to be aware of if this is something you have easily done in the past.
And then there is this notice on the Money Maxim website
As a Swiss-American (with a base and a car in the UK as well) I have opportunities others may not have. Not least because before I retired it was up to my Embassy employer to get me licensed and find insurance.
These days I mostly rent cars. I used to use one of my Amex cards but they only provide secondary insurance and when my hire car was dented in the parking lot of Fondation Pierre Gianadda at a cost of CHF 600 Amex only paid the 100 CHF deductible that my USAA insurance didn't. Now virtually my whole life's expenditures are on my Chase Sapphire Reserve card: free use of airport lounges, 3% back on restos and travel, primary collision cover on hire cars worldwide. (Such insurance doesn't cover liability, which is the issue in question.)
I personally know plenty of British licence holders who have moved to the USA or elsewhere and kept their UK licence. My son had his paper licence but it was so worn and torn and he needed to prove a UK address for some purpose. Swiss passport worked fine to prove his right of abode. He has no Swiss licence because he lives in the USA. Post-Brexit that might be harder except ... except his employment contract provides for NIC stamps to be paid (he has 34 years as of today). That had implications for EU/EEA/Swiss settlement too. One can be "ordinarily resident" in several places. Ask me: tax treaties don't save me from double taxation in every kind of income.
I don't know how many people keep both UK and Swiss licenses but it is not a few. I encounter many who spend half their lives in each country. Some regulations are simply unenforceable: imagine exchanging your licence every six months. My late spouse had a valid lifetime Geneva licence and a UK diplomatic one (these have a 3-year validity, renewable only so long as you retain status). US military are a special case: they get military licences.
Not so easy to pass the UK practical test after having driven for years on a concessionary permit. Ask me about driving in Manhattan. Back then we used to register and insure our cars in the name of a collapsible corporation (term of art). Insurance covered virtually any driver. Parking tickets ... are you kidding?