Well unless you have a EASA license you will not get it endorsed as a EASA TR, as you lack the fundamental things for getting that.
That's a EASA IR / ME / CPL.
Regarding the ATPLs, it all depends your experience level. I can't recall the details my friend told me about that, but you would have to have few thousand hours P1 time for sure.
The ATPL's must be completed within 18 months of sitting your first exam (passing first exam), and you IR must be passed within a certain time limit after passing your last ATPL exam (you need to check EASA rules) from passing your final ATPL exam.
When you took your type rating, you did not have a EASA IR/ME, that's one of the main reasons you can't endorse a license that you don't have.
When you do LPC / TR exam, that also gives you your IR. You can only get a EASA IR if you have passed the 14 exams.
Regarding the ATPLs, if I was you I would contact Bristol Groundschool, I am pretty sure they are clued up of what to do in case of Brexit. And probably have some contingency regarding this.