In our village almost all the children attend the local Primary school. A handful of parents (no more than a dozen) send/take their children to the RC Primary in a neighbouring village or a Private School some distance away. The policy is to include children with learning or physical disabilities in mainstream schooling with specialised support workers assigned, but there is one school in the County for children with more severe difficulties.
There is no 11+. All the children (bar the few mentioned above) progress to secondary in the nearest small town. It is called an Academy but is in fact a comprehensive, catering successfully for all abilities. Admission is based on the local catchment area, but requests for an alternative school are usually accommodated with the parents having to meet the travel costs themselves. There is little incentive to send children to an alternative school, as all the Local High Schools score much the same (excellent) in league tables. In general, parents and children assert that 'their' schools are the best.
All these schools are LA run and owned. Their is a proposal to remove charitable status from Private Schools, but I am not sure how far this has progressed.
This is, of course, in Scotland, which was, of course, not mentioned in the LP debate. In fact most of the proposals/promises on Education, child care, benefits, made in JC's speech have already been enacted by the 'left of centre' Scottish Government