I successfully sued KLM in Alnwick for something similar (cancelled flight leading to missed connections when they could have handled the situation better). KLM solicitors didn't show up in court, moaning on the phone that it would cost them too much to travel from London to Northumberland, I got the case on default, KLM's solicitors then sent me a cheque. It is best done in the UK small claims court, so I suspect it will depend on your parents' willingness to see this through. There is quite a lot of paperwork involved so while you could wait for the various appeal cases to go through I don't see any harm in starting the letter chase now. However begin with a clear request for the compensation without any direct legal threats. Customer Service may make you an offer giving you 50% of your entitlement for 10% of the trouble.

Fly BA next time. And get good quality travel insurance.