pretty sure you can "mot" in any eu country
I had a Portuguese contractor working for me probably 10 years ago. He'd been in the UK for a couple of years with his Portuguese registered LHD Seat when I asked him how he got on getting it MOT'd here. I got a blank look in response. I explained the details and advised him to get one booked just in case. They turned him away because the number plate wasn't "on the system, mate", so he never did bother. Nobody ever pulled him over.
Things have moved on. E.g in Spain the cops use zuK databases and impound British vehicles not taxed, motd and insured legally. Presumably UK can access other countries databases
Lots of EU reg cars a regularly pulled over, as they haven't been registered after 6mths,,, when in the foreign you must carry all paperwork relating to said motor to show it's legal in country of registration, same applies to non uk registered motors,
Your papers monsure, for me that means, Log book for unit and trailer, insurance, mot unit and trailer, community authorization, Cmr for load, trailer hygiene certificate, o and driving licence, CPC card, Digi card. And breathe