do you think banning choice in education would be enough to have the desired effect? it won't stop middle-class parents moving to areas with a decent school - unless you were going to award school places randomly and organise a (complicated and more than likely expensive) bussing scheme.
Rather interestingly, these bussing schemes exist in rural areas and the areas that still operate the 11+ system.
In either case then you have a choice between life chances being allocated either by chance, or postcode. The alternative would be to make all schools equally mediocre good, a major re-engineering process in itself.
Actually they tried this social experiment in the US to some extent, bussing in black kids into the subarbs and vice versa. It ended up working out really well. Outside of the rural areas, i.e. the cities, redistribution of pupils would merely mean putting them on the underused bus networks. It would cost very little in practise.
I don't think you've really thought that one through. And how would this address the other reasons for poorer life chances, such as addressing poverty and a culture of low aspirations, providing support to bright kids whose parents are unable/unwilling to help them academically, etc?
It shows them that they have a chance, which is more than a start. But in addition I would obligate parents and single parents on the benefits system to be doing something with their time, if they are not working they could be learning. This would then at least mean their offspring are not left behind, even if they were in the first place.
Of course I am not going to pretend that we will get a perfect system. However I feel we can get an awful lot nearer there than we currently are, in a very feasible fashion.