So as we're talking about non-EASA aircraft there can't be an answer for UK to EU but instead UK to individual country.
I'll try to give some insight on the situation UK to Germany:
It depends.
If it is an old "regular" aircraft but non-EASA type one would have to look at something called the "blue book"
https://www.lba.de/DE/TechnikUmwelts...ebersicht.html . If it's in there it could be . However the aircraft would have to be brought to a condition as certified in year dot by the LBA with only LBA approved modifications - which may be hard as modifications on a UK permit were much more common and easier as I understand it.
If it is a home built experimental (which I assume is the case here) - bad luck without rebuilding it and having the build inspected according to german processes for building home built aircraft.