Whatever the rights and wrongs of the UK's new school admissions policy, it will be a political disaster.
At present, middle class parents get their kids into good state schools by moving into the catchment areas of the best ones. So the plan is to allocate school places by lottery rather than catchment, so that poorer parents have an equal chance (and so that schools would get a wider social mix too).
While the parents whose kids get into good schools under this scheme will be pleased, they won't exactly be marching on City Hall to express their pleasure. But the middle-class parents whose kids don't get into nearby good schools will be absolutely furious, and campaigning in their thousands. And poorer parents whose kids don't get into their preferred nearby school will be marching alongside them.
And whatever the merits of the policy, its inevitable result is that kids will have to travel longer distances to get to school. That means they are going to be walking or cycling greater distances along busy streets, and (come winter) more are going to get killed or injured. Already there is a spike in road fatalities around the age of eleven, when kids transfer from their neighbourhood primary schools to the more distant secondary schools. The first case of a kid being killed on one of these forced cycle trips will get the media, and parents, baying for ministers' blood.
A better policy would focus on incentivizing state schools to improve, not rationing them by throwing dice. For some ideas, ministers should check here.