welcome to FT, I hope your father's health improves.

Sadly I doubt BA will be sympathetic, but I hope you understand that if they didn't automatically allow flexibility on non-flexibility tickets then the lower moral fibre of society would invent 'family emergencies' to get a refund.

Your travel insurer would be the place to turn - most include coverage of immediate family members. If you don't have an independent insurance policy it's worth speaking to your bank or creditcard issurer as some offer travel insurance as part of the account (but obviously you'd probably already know if you had insurance via your bank).