Flying keyboard,
Yes, there will be. But what?
The obvious solution is for the UK CAA to recognise your training and give you an NPPL SSEA. At least that will allow you to continue to fly in the UK.
Question: will the CAA have got its act together - or is it even allowed to do anything while part of EASA? - and negotiate with ICAO to make the NPPL SSEA (or a brand new old-fashioned UK PPL A) an ICAO compliant licence that you can later add CPL etc to?
Maybe we should have a wiki to pose some of these questions and possible answers.
For instance, will UK airspace close on Brexit plus one? ATC have EASA licences! Will many airlines be grounded with many of their pilots having UK CAA issued EASA licences? How will transatlantic stuff re-route?
Will it matter if UK airspace is closed for a week or two while temporary solutions are fudged? After all, the world never came to halt when the ash clouds shut our airspace for weeks.
As you can see, I feel all will be OK for the Big Boys. But what about the Small Fry like FKB?
FKB: ask your flying school. See what they say!