Hello,
I am not sure it can compete with private schools - if you have colfe's I would take Colfe's, same for Blackheath High. But it depends upon the money. Private costs will just keep going up. If you have a place I imagine you live close so a shorter distance for your child to travel is always a consideration.
Parents are pretty desperate for a place there, I do know that!
I too don't have children going but I know one child there really well and also know the parents. They seem happy and of their child's friends seem really lovely.
Other people I know more generally always seem happy enough with the school. Have heard that they have a lovely library!
The school seemed very clean when I visited and I seem to recall hearing good things about the head.
I don't know what you do about results!
I suppose it depends what you think. I don't think it can compete with Colfe's in terms of pastoral support and grounds.
What I would say is that other state options nearby are challenging, like John Roan. Greenwich should be better served with secondary schools.
Also if you do stay private make sure you decline when you really know -other people will be desperate for a place.
Good luck!