*Where I come from in Germany children just attend the nearest school, all the schools are the same and there's enough room for everyone."
Same in the US, where I grew up. And Scotland does it. I've never understood the resistance to catchment schools here. It's probably a reach to claim "all schooLs are the same" but catchments do seem to produce better equality than the British system. Over-subscribed schools become over-crowded, hence less desirable, and to some degree things even out.
Ideally all schools would be equal - but that's a long way off.
For now, in Haringey, let's be honest. People in CE live in a naice area and expect to send their children to naice schools. Many in Tottenham don't have either choice. Some Tottenham schools are decent, others are dreadful. And these days there are primary 'black holes' in parts of Tottenham, too.
Haringey has a number of crap schools and I don't hear many residents of Crouch End worrying about that.
Finally, keep in mind the lesson of Downhills - traditional dump school, got a good head, became popular, Gove swooped in and forcibly converted it to an academy.
It's well known many Haringey schools face forcible conversion to academies in the next five years. This includes some oversubscribed schools in Tottenham. The naice CE schools are probably secure. I'm no fan of Haringey Council's education dept but in the current circumstances, and given what happened to Downhills, I could hardly blame them for just giving up.