The UK Government is still negotiating an overall trade agreement with the EU, the terms of an agreement covering passenger transport have already been settled, and details will be updated when or if the trade deal is finalised.
However, irrespective of the authorisation being used for an International Journey a valid test certificate must always be carried on the vehicle.
DfT realise that this may not be possible where the annual test expiry for a vehicle has been extended, and has shared information with the European Commission.
Therefore, they have produced a letter that should be carried on the vehicle and a print of the vehicle record from the https://www.gov.uk/check-mot-history service showing the extended expiry date.
Link to letter: