CD, as you may remember from other thread last time you looked at moving, my parents and siblings live in Winchester and I was brought up there (before I escaped to live in London, land of endless coffee shops, cheap local restaurants, multi-ethnic living, grime and f*ing unreliable transport) .
FACT 1: house prices are cheaper than London, but still pretty pricy, particularly in some "brackets" - notably people moving out of London with small children. M&D are looking at moving and had some particulars which I was looking at at the weekend and I was sort of - but not very - surprised at prices (I know an excellent Victorian/Edwardian detached house in prime location for sale, if you are interested ).
FACT 2: Winchester is not the countryside, therefore arguments re not spilling out money on cappuchino's etc does not hold good. Conversely there are not that many nice places to get cappuchino's.
FACT 3: I believe good childcare, while probably a bit cheaper, is harder to find - not the same market and availability as there is in SW London.
FACT 4: State schools are largely v good there and will be your major saving (I was entertained that the one I went to was listed prominently on particulars of houses for catchment area purposes). Don't know how old your children are, but my mother (retired teacher in local state school) said some were getting horrendously difficult to get in to, so you really need to do some due diligence before moving down there re whether you actually will be able to get your children in.