I will relate my personal experience moving cars around.
As a UK passport holder resident in Africa, purchased a car in France, collected it on one of my trips to the UK and drove it to the UK on French insurance and plates. I was stopped at the border and asked if I was permanently importing the car or re-exporting it, I was non committal and was told I had to do one or the other within the defined period. I drove it on French insurance for 6 months until I submitted it to be checked for registration.
Before moving to France, so as a UK resident, I moved 3 vehicles to France, all were used on UK plates with French insurance and CT within a short time of arriving until registered. My MR2 remained on UK plates and French insurance and CT for 3 years as that was how long it took me to get a special derogation from Paris for car that had never been homologated in France. Again no problem.
Later as a French resident, I imported a Renault from Belgium, no problem getting French insurance so I could go by train to collect it. Later still I imported a Citroen from the UK, then a Transit and a P38. In each case I got French insurance on the UK plates even though the vehicles were not registered in my name in order to collect and drive the vehicles back, in each case I got a CT on UK plates and a quittance fiscal to start the French registration process.
Things have changed since Brexit, but I see no problem in driving the car back to the UK on French plates and insurance. A bill of sale would be needed as proof of ownership and UK VAT & duty would be payable.
