It look is like Brexit will really happen on October 31, with or without a deal. There are various webpages with updates (British Consulate in Madrid and Gov.UK being the main ones) and Nexonr will also keep you up to date.
This is the latest information from Gov.UK on driving licencs and MOTs.
You must exchange your UK driving licence for a local EU licence to drive legally in the country you live in. You
must do this before the UK leaves the EU.
Exchange your licence as early as you can because your application may take
longer than usual to process.
You will still be able to drive on your EU licence when visiting the
UK.
Also remember your
UK MOT test certificate will not be recognised in
the EU after Brexit.
You must have your vehicle retested in the EU country you live in.
Published 12 August 2019
