I think the most important advice is not accept a cancellation/refund of the tickets. Then BA and EasyJet are off the hook.

Presuming that the EasyJet tickets were more expensive than the BA tickets, you request full reimbursement of the rEasyJet tickets from BA, but obviously, you are not entitled to a refund of the BA tickets as well (hence, it was wise that you declined the BA suggestion to refund the tickets).

You have plenty of time to file the claims for reimbursement and compensation. Do that once you are back in the UK; now it is about getting to Antalya and enjoying your holiday.