There has probably never been quite so much contact between independent and state schools as today. In my youth, my direct-grant grammar school was in the same quadrangle of streets as the prestigious fee-paying Birkenhead School. In seven years there, I do not remember a single shared lesson, meeting or social activity, if you do not count occasional joshing at the bus stop where, I seem to recall, the toxic word “plebs” being uttered regularly.Nowadays, by contrast, private schools bend over backwards to forge stronger links with local comprehensives – if only because they are now anxious to prove their “community benefit” in order to retain the taxpayer-funded subsidy that comes with charitable status. That may sound unduly cynical, but in the fee-paying e