I would not hold out hope of BA refunding. I had to cancel a trip due to Mr HH's cancer*. BA refunded the taxes, travel insurance picked up the rest. Mr HH (i.e. patient) and I were due to travel

BA were sympathetic and kind on the phone, but were politely clear that as I had booked a non-flexible, non-refundable ticket, they would be sticking to the terms (as I expected).

* I swear Mr HH has a medical-personnel-addiction. We now only book trips a few weeks ahead of time! Wonder if a poster of a nurse would keep him out of hospitals better