You will still need to carry your driving licence with you, but UK drivers may also need an international driving permit (IDP) to drive in some EU and EEA countries from 1st January 2021. Please check the government websites of each country you will be driving in for up-to-date requirements.
If you are driving your own vehicle, you will need a 'green card' as proof that you have motor insurance cover and UK drivers will need a Great Britain (GB) sticker on the rear of the vehicle and trailer when driving in the EU. UK drivers will need to display a GB sticker even if your vehicle has a number plate with the Euro symbol or a GB national identifier. UK drivers do not need to show a GB sticker to drive in Ireland.