They won't because they don't know who you are. That is the problem, they can't contact the UK authorities to request the driver's details so nothing will be attached to your record.
Biggest road trip I've done was Leeds to Ruse, Bulgaria and back in 2015. Leeds- Épernay- Aix-en-Provence , Avignon- Genoa- Florence- Bologna- Slovenia vineyard- Zagreb- Belgrade- Sofia- Ruse Way back: Ruse- Bucharest- Bran- Timisoara- Budapest- Nuremberg- Rhine valley somewhere- Bruges- Leeds. All in an old Fiat Grande Punto. Broke down on the motorway near Aix and managed to get the car to a garage and get ripped off for repairs due to my language limitations. Apart from that, was amazing. And Aix isn't the worst place in the world to be stranded a few days to be honest
It was either a hire car - in which case they know who hired it - or his own car - in which case it'll get pulled over and the owner having his cavities searched if it goes to Estonia again... Although the DVLA database is publicly searchable, and the DVLA will supply the information on request.
Lad and Partner do Airbnb london. It certainly helps with the mortgage. Taken up most weeks. Only leaving some time for themselves (lad is on shoot a lot round the country) and family and friends. To visit.
I was surprised as to how much information is available to anyone. Driving down Hound Hill Lane towards Rockley Bottoms very early last Sunday a car parked half on road half on banking - stopped to look - windows open - no sign of driver - phoned police thinking driver may have been injured - wandered off - they didn't wan to know - advised that 'all abandoned vehicles have to be reported to the DVLA' - google DVLA and they want the tax and MOT status of any car reported - this was surprisingly easy to find - just key in registration number on web site and information is there. (Of course no one at DVLA on a Sunday !!)