I would argue in respect of BA is that if the ex represented to BA that he had the right to cancel on behalf of OP, and BA now knows that to be false, they have a right of recovery of any loss against the ex. However they have nothing to recover because they have the ticket price anyway.

Here the cancellation is a binding obligation on the principal in respect of a contract, giving up her rights to insist on performance for carriage. It was probably made with apparent authority, but the ex had no express or implied actual authority as an agent, as that would have been terminated by the break-up.

As such, the cancellation was never validly made and BA is wrong to be insisting upon it, effectively acquiescing in or participating in the fraud perpetuated by the ex. (Admittedly the Ts & Cs may deal with this, but I would argue that anything that requires you to give up your rights to be protected from fraud, when the airline has suffered no detriment, would be an unfair contract term).