They may not be selling tickets, but they may still have space. Heathrow have asked BA not to sell tickets.

Have you or your family spoken to BA? I can't help feeling that would be more fruitful than asking for general advice here, as they will have specific information on what is available.

Note that the protests would have been the XR ones that closed the M25 and stopped a lot of traffic, including, I suspect cabin crew. Not an ongoing strike, though these things do tend to cluster when they start.