A BA contact centre will never rebook you on to another airline. (only on v. v. v. rare occasions such as the strike where there was a lot of notice and the potential for the entire operation to come to a halt.)

The reason for this is that too many mistakes are made which cost money.

BA airport staff however, will do it without batting an eyelid.

Lesson: If your flight is cancelled, just go to the airport and get it sorted there.