EASA is an agency of the European Union and may be unwilling to issue licences on the strength of a non member country's aviation authority. Perhaps the old CAA Licence will be reintroduced and pilots wanting an EASA Licence will need to do the tests in Europe.
Employing UK nationals would be less attractive for low costs with multiple bases across Europe as work permits would be needed. Any British based low cost operating intra European flights needs to start thinking about its future base of operations.
Britain has always had a trading relationship with the rest of Europe, it will be interesting to see what form the new one will take. Malaysia kicked Singapore out in 1965, on its own Singapore has done far better over the last 50 years.