Of the Oxford City schools, Cheney was a Grammar, which is now Comprehensive, but I don't know what its reputation is. What is now Oxford Academy has had an extremely chequered history, having been turned into a comprehensive by combining Littlemore Grammar and a couple of Sec Mods, into Peers School, which went rapidly downhill, until its rebirth as the Academy, and now appears to be on the up.
For Catholics there were the Salesian College for boys, which was run by the Salesians, but was basically an independent school being propped up by the scholarship boys (according to DH who went there) and Notre Dame for girls. Both joined up with the Sec Mod and became Edmund Campion comprehensive, (now something else).
Oxford High started its life as an Independent school, became Direct Grant and then went Independent once the comprehensives came in. I don't know Magdalen's history except that its been going for a few hundred years.
In a nutshell the ex-grammars which have become Independent have had a much longer history of being Independent than they ever had as grammar schools. The Local Authority Grammars have disappeared.