I sympathise Sydenhamhiller, we faced same issue a few years ago. But as Sandy points out our 2 local schools have 66%ish good GCSEs. A result that is more impressive when you consider these schools serve the whole of this wonderful but mixed area.
First thing I'd say is don't think in terms of right and wrong answers. All answers have pros and cons. Don't get too alarmed at the flight to Bromley and beyond - it may look appealing but doesn't work out better for all.
If you're committed to this area, I agree with Kingly - we have good schools on our doorstep (I mean FH Boys and Sydenham Girls). Our kids went to both. Oldest now at Russell Group university doing a "real" subject. Middle one has achieved A* GCSEs early. Youngest also loving secondary school. Both offer so many opportunities (Latin, music, rugby, author visits...) and because they're local schools, your kids can take advantage and still get home at a reasonable time (or get there for before-school activities).