Would Lufthansa or KLM not work as alternatives – or do schedules not suit? I know they get in middle of the night?
My guess is a refund due based on the highest fare charged on a CE route operated by a Shorthaul 767 (IST without doing extensive research?). Based on IST a full J fare is £1212 return. So if you paid £4800 that leaves £3600 as extra paid. Assuming 767 shorthaul was one way then minimum refund due should be £1800 and then some compensation on top (avios or money).
Edited to Add: LCA is slightly longer and full J is £1500 – so same maths gives £1650 as an amount possibly due. This would be my starting point in negotiations with BA.
Only a very quick calculation – but one which would seem logical.