It's a standard marketing technique to encourage you to complete your customer journey through to booking your flight. Anyone hanging around on a booking screen for longer than a pre-defined period of time, should get the pop-up just in case you might need some help in converting your interest into a real sale (assuming someone in the call centre is available).

And I agree it's a good "enhancement" to ba.com. Better than some of the so called "enhancements" elsewhere.

The annoying thing about this live chat mechanism is if there is a delay before the call centre agent is available to provide support.