BA F bag drop is normally strictly policed so it should take no more than 5 minutes in the queue.
F security is strictly policed and I have never waited more than 30 seconds. As a BA F passenger you get to use the JL fast track near the BA check-in rather than the standard OW fast track one that's quite a bit of walk from the BA check-in.
Immigration is an unknown factor - anything from 2 minutes to 15 minutes is my experience with BA 006.