As I understand its not possible to have a EASA licence and a UK licence (or even apply for a UK one) until we have left EASA.
It is - I hold both.
So far small piece of advise: THE EU has no fear about uncontrolled exit, highly recommend to look for an EASA licence if possible.
Outwardly no, the institutional view appears to reflect that, however internally I understand there is considerable concern about a no-deal exit and hence the proposed regulation. Many in the EC and dependant institutions have believed that the UK will never completely sever ties with Europe and indeed the UK Government has certainly given that impression since Article 50 was invoked, but a discussion I had last week with a trusted UK aviation manufacturing industry management source suggests that this political wavering might be a strategic ploy to force the hand of the EC and bring them to the negotiating table with a view to leveraging more favourable terms for the UK. From the perspective of the aerospace industry, and leaving the soft assets aside, how many UK manufactured and certified components are flying around in or hanging from EASA registered aircraft flying today and for the next many years?