Elephantstrunk

Approximately 90,000 children are in the process of transferring from London’s 1,836 primary schools to its 406 secondary schools. Each student may apply to up to 6 secondary schools in an order of preference.

Each school will determine an order of preference for those children that have applied. In most cases it will depend mostly upon distance from the school but might also be based on test results, religious affiliation and stated preference.

As far as I can tell the process works as follows. When all the application forms test scores and distances from home are in, students high enough in the order of preference in their first choice school to be guaranteed as place are assigned to that school are assigned that school and removed from consideration, the number of places at each school reduced appropriately, the orders of preference correspondingly revised and the exercise repeated.

That appears to be, in effect, a Gale Shapley Mechanism. It therefore has the property that there is no reason not to put your preferences in the true order.
That is a good thing and quite amazing since it is not decreed by a central authority but coordinated at least partially from the ground up between the 32 boroughs. As a result it takes six weeks to perform and children will not know which school they will go to before March. This is surely begging to be properly automated.