In the lead up to Brexit all the expert opinion was that Green Cards would be needed as evidence of insurance to drive in Europe.
We had the 2 false starts when Brexit was due to happen but did not, and at those times Green Cards were considered essential.
Well now Brexit has happened, on 31 January 2020, and we enter the 'Transition Period'. During this period the UK is still subject to EU law and as such our normal car insurance is automatically valid throughout Europe, not just the EU, but Switzerland, Norway etc as well.
So the answer is that until 31 December 2020, or whenever the Transition Period ends, you will not need a Green Card to drive your vehicle in Europe. And who knows what will happen after that?