The policy is that the fare rules continue to apply to the connecting flight, and if you miss it because of a late incoming flight, you may forfeit the ticket.

However in practice, BA may take a flexible approach, and again I think your value to BA will play a role.

You may be accommodated, without a penalty, on the next available flight. Or you may be lucky enough to be re-routed on another airline, inspite of the original fare rules, if BA really wants to get you there on time.

But best not rely on this.