Short answer to the original question is - Yes, BA will hold an aircraft. BUT there are a multitude of considerations and it's rarely the discretion of the local airport, as they don't have visibility of the bigger picture.

Aircraft: What is the knock on effect to later flights operated by that aircraft if it is held?
Crew: Are crew operating further sectors / close to working hour time limits?
ATC: Is the flight subject to a slot?
Airports: Will later sectors be subject to curfews at airports and risk cancellation?
Flight Plan: Does this flight plan have a shorter than scheduled time due to favourable tail winds?
Recovery: Can these customers be easily recovered on later services?
Onward Connections: Will holding for these inbound connections jeopardise other customers with onward connections?
Flight Documents: Does offloading these XX customers result in significant weight and balance issues requiring new flight documentation?

So Yes, BA will hold aircraft. If it makes sense for them to do it on the whole. But the instruction usually comes from Operations Control and not the airport.