This happens to all of us at some point, if you make enough bookings at some point this will happen. BA have often stated that they will not seek to profit from obvious booking errors, and in any case bookings within 24 hours can be cancelled for a full refund - best to call for that. But there have been cases where for whatever reason it is spotted after 24 hours and BA is still OK to refund this sort of event.
Alternatives to calling include using the chatbot and forcing it through to an agent to be online, or using a Direct Message on Twitter, but telephoning is the best thing to do.