Edinburgh has in the last couple of years abolished the "assisted places scheme". This was a scheme where brighter pupils could apply for a grant to go to one of the many independent schools. The result, as far as I can see, was to bolster the results of the independent schools, by extracting many of the more able and better supported children from the state sector. This had the effect of making the results (we have league tables, based on examination results) for the state schools look even worse and making more parents keen to raft their children out. I suspect that the voucher system that you describe would have a similar effect.
In the UK in general there are very many excellent state schools. The problems tend to arise in places like London and the South East and Edinburgh where there is a long history of take up of independent sector places. In Edinburgh many of the state school buildings are poorly built and lack facilities - the school that my children could attend does not have a playing field, level or otherwise. I don't have any evidence of the children from independent schools in Edinburgh being any "less rounded", to my surprise, quite the opposite.
There was an interesting article in the Guardian last week which claimed that many of the results from state schools in London are skewed by parents paying for tutors to improve their children's results. I tend to agree with this as I have often heard my "professional but liberal" friends in London discussing where to find a good tutor, my "professional and less liberal friends" spend their time comparing independent school results.
http://education.guardian.co.uk/schools/story/0,5500,680734,00.html It stikes me that, much as I dislike it, the "level playing" field concept works against the laws of human nature, where people are in favour of it until it starts to cause problems for the future levels of achievement of their own children and they have to put their hands in their pocket.
There was a report yesterday that some pupils were moving back into the state sector as Oxford and Cambridge were committed to increasing their intake of state school pupils, it remains to be seen if this will have a long-term impact. {I'll add a link to this news story if I find it.)
