Cranbury, I can understand your views on state schools given your own and your husband's experiences, but I do just want to come to the defence of Winchester schools (even though you've not been critical of them). Winchester is an odd place in a lot of ways. One of the ways to understand that is to just look at some of the online estate agents' pages and see what prices properties here reach. In terms of square footage, the house prices are ridiculously high in many areas both within the city and in some villages outside.
What that means is that many people find they can't afford to buy properties (or even rent) in this area, unless through the local authority affordable-houses scheme. What that also means is that those parents who can afford to buy here are generally (but not all) those who have aspirations for their children's education. And what that means is their voices are amongst those of all local parents who have aspirations for their children's education.
There are a couple of primary schools who have catchment areas that might include several supported families but, not only do they also get good results, if you're relocating from London, your budget would mean that you wouldn't be looking in those areas anyway unless you're looking to downsize.
Primary schools in the city and the surrounding villages feed into the comprehensives, which feed into Peter Symonds (which has a huge catchment area). For the end result of state education here, it's worth finding the statistics for Peter Symonds. From memory, there are a number of PSC pupils who have gone through state education to Oxbridge.
Winchester house prices might make it look like a snobby, middle-class area, but ever since the build-up of council estates in the decades following the last war (yes, I almost go back that far!) there has always been a mix of private-house-owners-who-couldn't-care-less and council-house-renters-with-aspirations-for-their-childrens'-education. Just as it was back then, so it still is now. Well-rounded education is pretty much what Winchester has been doing for very many decades, and still is.
Spend a little time down here, and look at the state schools.
Actually, I wonder if I could do a quick survey of mums at the local primary school (a way up the road) or the local secondary school (slightly less up the road but just round the corner) and see how many of them wear Boden. (That's me being a bit sarcastic, by the way.)