No. As the UK has negotiated a deal to leave the EU there will be no changes to the current rules for UK drivers travelling to the EU.
Cover is provided in the following European Countries:
Andorra, Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France (including Monaco), Germany, Gibraltar, Greece, Hungary, Iceland, Italy (including San Marino & the Vatican City), Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of Ireland, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden and Switzerland.
You will also need an International Driving Permit. You can find out more about getting an International Driving Permit by going to the UK Government website on driving abroad here: https://www.gov.uk/driving-abroad.
We also advise that you carry your Certificate of Motor Insurance with you when travelling. You can view your Certificate of Motor Insurance by logging into Your Insurance Account