Kids travel much further for secondary school than primary and many don't use distance as a criterion for awarding places, so your options are wide open, really, you don't have to stay in borough. Anywhere in London, take your pick! Local population sizes don't, therefore, have the same impact on secondary schools.

There are grammar schools as well, worth looking at if you think that would be something your child would benefit from (most won't). There are four in Bexley, some in near Croydon and some further out in Kent and Surrey. And if you're Catholic, there is a wide range of school spread across South London (West and East) and out towards Croydon and Sutton.