I visit a lot of schools as part of outreach work and some of the least likely are so open and willing to discuss how best to help their most able pupils. Then others, considered 'better' schools are just awful. Closed minded, resistant to new ideas and taking decisions which actively harm the ongoing opportunities for the most able.
I completely agree with Eric on this - it is very depressed when one goes into such schools.
Somewhat related to this issue: we live in the catchment of a comprehensive with very skewed demographics (lots of academics, doctors, London commuters) in which 5/9 sets are high achievers and 3 or 4 sets would be grammar school material.
There are grammars about 20 miles away across country borders. We could have moved to them. They all have a reputation that many kids are heavily tutored to get in - I suspect they are taking broadly from the top 30% in ability terms, i.e. their cohorts are pretty comparable with the top 3/4 sets in our comp. The top 4 sets of our comp actually out perform the grammars and the grammars don't seem to offer more academically, so we never considered them. I also have had the impression that these grammars are very rigid and not willing to change what they do, as Eric says above.
Since the comp has such high results you could wonder why we looked at independent schools at all - but the issues are that they teach a relatively narrow curriculum, and don't have the resources to offer opportunities such as Olympiads to the most able. They rely on parents to provide extra-curriculars and co-curriculars.
So while DC would probably have gotten good grades in this school, we looked at privates for a deeper and broader curriculum. We looked at three privates: (a) top 10 in league tables, (b) top 40 and (c) top 100. We didn't feel there was much difference in what was being offered to the highest achievers in the three schools: (a) and (b) are further up the league tables due to being "big name" schools and hence more over-subscribed. Both (a) and (b) effectively re-select at 16, explaining their high A level results. The top groups of (c) do just as well, but they don't select so heavily so their overall average results aren't quite as high. We actually felt that (c) was the most flexible and the most willing to offer something extra personalised to our DC.
BTW we could have also have changed jobs and moved to a superselective grammar area (but I am pretty unconvinced by the teaching and atmosphere in these particular schools), and we could have moved to the US and accessed a gifted program. But the latter are not usually particularly terrific: they can have arcane entry requirements and often don't offer as much as top set kids in the UK get.