Yes, as of 1 January 2021 you will need a physical Green Card to travel in the EU. A digital copy on a smartphone or tablet is not acceptable under the Green Card system. Your cover will remain the same.
You may need to display a GB sticker on your car.
You should take your log book (V5C) and other similar documentation with you if you're leasing a car. You might also need an International Driving Permit (IDP) to drive in some EU countries and Norway if you have:
- A paper driving licence
- A licence issued in Gibraltar, Guernsey, Jersey or the Isle of Man