You will still need to carry your UK driving licence with you, but you 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 a Great Britain (GB) sticker on the rear of the vehicle and trailer. You will need to display a GB sticker even if your vehicle has a number plate with the Euro symbol or a GB national identifier. You do not need to show a GB sticker to drive in Ireland.