Airline-initiated-cancelled is indeed a very different question but that's not what I'm talking about - lots of threads on what happens if you want to cancel too. I'm on the phone and on the move so can't really do the search for you, but I'd suggest doing a google search with things like "flyertalk british ariways cancellation policy" and I'm pretty sure you'll get some results.

If you are sure the ticket is non refundable though, then indeed, your options are change or get taxes back minus fee.