I can also confirm that this usually works. Last year I had a delayed flight which led to me missing my original connection at LHR (route was HND-LHR-LIN). I had been moved to the next following LIN flight by the time I arrived at HND, as the delay was known, but by the time we landed there was 50 minutes to make the connection from T5C to T5A. We did not have any major difficulty.

Assuming your full journey is on a single booking, BA/CX will sort you out if they cause you delays.