I speak from personal recent experience in saying that BA can be very sympathetic in circumstances similar to this. Mine wasn’t as complicated, it involved illness rather than a bereavement, but I was placed on a flight back to the UK that was closed for sale two days before I was supposed to return. My original selling class was not available, but BA placed me in full fare Y and didn’t charge me a penny. Being Gold helped in terms of the burden of proof needed, and clearly it might depend on whether the death the OP is sadly having to deal with is of a close relative, but I agree it is well worth fully outlining the situation to BA to ask what options there might be.

This isn’t even asking for a goodwill gesture - BA has a number of different policies they can apply. One of them might just fit.