websites and organisations associated with taking one's car abroad (e.g., The caravan Club) are already advising precautionary measures for any UK drivers being in the EU after March 29, 2019.
I have now obtained my International Driving Permit and the Green Card from my insurers, and our travel insurance is covered by Red Pennant (a subsidiary of The Caravan Club).
What I did learn, and this may be of interest to drivers, is that if you are towing anything (caravan, boat trailer, trailer tent, etc.), you also need a separate Green Card for that towed item. The GC for the car is category A, and for the trailer it is category F.
I mention this because, when dealing with an insurer's operator, I can imagine some operators not being aware of the GC for a trailer, or a driver failing to say that he/she will be towing.