No refund for checked baggage payment

I have had the worst experience with Booking.com I booked flights from CT to London return, upon checking our return flights I noticed that our checked baggage was not included. I contacted Booking.com who informed me there was a technical error and I should pay the airlines then they will refund me. I am now still waiting for a month! Initial call was 18 July, they said 1-3 working days refund, then 2 weeks ago it was 24hrs hrs, Friday it was 24-48 hrs. Today… they are still investigating and waiting for British Airways to refund them so they can refund me. Can someone please guide me as to how I can escalate this?