People do leave forest hill for other areas such as beckenham when their kids reach secondary school age but it is far from a trend. I don't know of any families who have made this move, only anecdotally. Even when the property market was buoyant I didn't see evidence of people with secondary age kids leaving the area in significant numbers.

The local secondary schools are good, have improved and continue to improve. My only issue with secondary schools around here, and in London in general, is that they tend to be single gender. But I only have a problem with that as it is not what I grew up with and it means my kids will go to different schools.