British Airways & Aer Lingus Refund Hassle, Canceled Flight

I bought a return ticket from British Airways to Aer Lingus for Belfast. Unfortunately, our return flight got canceled. We had to purchase tickets from a different airline because the alternative flight they provided overlapped with our return to Turkey. Even though we submitted all the required paperwork, they haven't given a favorable response to our request for compensation. I would like a refund for our ticket purchase. It has been two months, and they are still delaying.