British Airways dragging their heels after written promise of a refund (2016) - can I complain/escalate? [closed]

TL;DR

1. I booked flights mid-2016 (with British Airways via Tripsta)
2. I became pregnant
3. I was advised by doctors not to travel (see Zika virus)
4. I cancelled booking (note: flight wasn't cancelled)
5. I received written promise of refund (from CEO's complaints team)
6. I get passed to-and-fro between British Airways and Tripsta, none of which claim responsibility for refund
7. no refund materialises
8. I give up mid-2017

That was 3 years ago:

• how can I get British Airways to follow up on their written promise of a refund?
• Is there an ombudsman? (UK)
• Is there an official body that I can complain/escalate to? (UK)

Details

Back in the summer of 2016, we booked a flight from UK to Mexico via Tripsta. Both the outbound and inbound flights were with British Airways.

We became pregnant, and became ware that Mexico was considered one of the at-risk regions for the Zika virus, which presents a threat to the development of foetuses in-utero. Therefore, we were advised by our doctor not to travel.

The flights were cancelled on medical grounds, an explanation given to British Airways, and a written promise of a full refund (inc. taxes) was given, direct from the British Airways CEO's complaints team.

But since late-2016, I was passed to-and-fro between British Airways and Tripsta who both were passing the responsibility onto the other: British Airways would say that Tripsta originally took the payment and so would have to pay the refund; Tripsta were saying that the money would have eventually gone into the British Airways coffers, and so they would have to pay the refund.

After about a dozen calls, 4 letters and all the time that entails (and now with a newborn), I just couldn't muster the energy to pursue this. So I temporarily left it there.

Now my boy is 3 years old, so I have a bit more time on my hands. So I'd like to try again and get my £500+ back!