OP,
(Now happily retired :) ) I taught at John Fisher and several of the public schools in Croydon and South London between 1985 and 2009. I was on the board of governors at John Fisher for a time during its selection policy.
Your DH could well have been taught by me, and I was quite possibly among the senior members of staff who interviewed him and his parents at the time :)
The education landscape changed considerably in this part of England post-2008, where a culture of supertutoring now prevails. Prior to this John Fisher, Coloma Convent and a few more leading faith schools used to select pupils at 10+ interview, which appealed to parents turned off by the culture of tutoring and pressure created by the presence of the few grammar schools in LB of Sutton, which select in a very narrow and unforgiving manner it could be argued. The selective faith schools also looked for talent in sport, music and the arts, so were attracting all-rounder types and children who otherwise might have ended up at Whitgift or Trinity. At John Fisher we recruited at 10+ intelligent, articulate young men with the use of interviews with the boys and parents, primary and prep school reports, and written applications from the boys. We also conducted a short written exam for Catholicity, which we would then quiz the boys on. The composition of the boys selected was usually around 30:70 (private prep school:state primary). Prep school boys were drawn mainly from Laleham Lea (the traditional feeder to John Fisher located on the same road). State primary school boys came from far and wide - even a few from as far away as Edenbridge & LB of Bromley (West Kent), Inner London Boroughs, Surrey, Sussex. John Fisher sent boys to the best universities, achieved pass rates usually in the region of 75-95% in any given year for boys achieving 5GCSEsA*-C.
Inevitably with the disadvantage the 2008 Code put the leading comprehensives at (the 5 grammar schools in Sutton, Kingston and Bromley now creaming-off the brightest boys) these schools have suffered. Where once John Fisher could compete on the rugby field and in the exam hall with the best independents, this has gone by the wayside somewhat.
Whitgift is a lovely, inspiring school. The overwhelming majority of boys and parents are conscientious, hard-working, committed to the school, its aim and ethos. The loutish chants and handbags at their rugby matches are, I expect, a small minority of a certain type of parent found at most public schools.