Lots of great advice as usual on here.
My thoughts are exclusively related to schooling, because that's the thing that caused us the greatest headache.
As with other regions, but even more so in London, as Kirsty and Phil say 'location, location, location'.
If you cannot afford private schooling, then for primary, if you want an ofsted 'outstanding' rated you need to try to buy a property very very very very close to the school. Year on year, the catchment areas shrink, so that in many cases, it's just a few streets (sometimes just parts of those streets!) surrounding the school. This is because once one child is in, the sibling priority rule can take up the majority of places in a reception intake. This is hurdle 1 with schooling. Hurdle 2 is secondary education. You may find yourself in a brilliant primary catchment area, but the choice at secondary not good at all. Many people need to move again for that stage.
If you have managed to buy literally on top of a superb primary (which remains superb), your property will usually sell easily. Estate agents can have long lists of people waiting for these properties. This can affect property prices such that houses/flats close to the best schools are considerably more expensive than ones in say a street away, but out of a particular school's catchment.
With a 2.5 yr old dc, and reception intake at age 4, if you can't afford private, this would be a big consideration if it were me.