You might have more luck if a spouse or child needed surgery. (I've had several vouchers for my own all-too-frequent surgeries!) But as you say "relative" I assume that is not the case. You'll probably end up having to pay the change fee and fare difference unless you have a somewhat flexible ticket. You might try doing a test booking for the dates you actually want and see what the fare difference is to give you an idea on costs. If you have some flexibility of a day or two and/or can fly at different times of day, then being armed with the cheapest option before contacting BA is a good idea. You might try the chat on the website as well. Wait times can be long on a weekend, but you'll usually get through eventually. And maybe you can wait until Monday. And using the chat to copy and paste the flights you want might be easier than reading them off over the phone.