The future for British Pilots in Easyjet and other British Airlines is far more uncertain than is suggested by the optimistic posts above. Until there is a deal, no deal still being very possible, it looks likely that the UK will drop out of the transportation agreement. The repercussions of that situation would probably be very serious as scheduled flights from the UK into Europe would be subject to bilateral agreements and opposed vehemently by foreign flag carriers and Ryanair. I also don't see airlines lifting the right to live and work in the EU as being an prerequisite to most LCC jobs.
I understand that bilateral agreements work both ways but there will be long term vehement legal opposition from parties such as Air France, Lufthansa etc who already have their bilateral in place and who would have a great opportunity to restrict opposition.