The below Brexit update has been published  12th August.
UK and EU driving licences

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.

Link for driving licence exchange:

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.

Vehicle safety and roadworthiness MOT

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.