Nermine, I think you assume that London is a city with some distinct areas with good schools. London is 32 different boroughs and all of them are mixed, with some areas in a borough having more good schools than others.
However, to reiterate what earlier posters have said, it's not about where there are good schools but about where there are good schools THAT your children can get into. For example, there are a number of very good Catholic schools, but if your children are not Catholic then they will have no chance of getting into them so they are not relevant for you. Similarly, at second level (starts September after child turns 11) there are grammar schools, which only take children that perform highly enough on an entrance exam, but unless your child is able to do the exam and perform highly enough to get in, they are not relevant for you.
For independent, i.e. fee-paying schools (and assume cost of minimum £12,500 per year per child for fee-paying school), location is only a case of how convenient it is to get from where you will live to the school. However, almost all state schools base admissions on distance, i.e. if more children look to get in than there are places, those nearest the school get admitted first (assuming also, in the case of a religious school, that they need the religious criteria).
Another poster has asked for your housing budget because obviously there may be areas of London that would simply not be affordable for you and that would also be ruled out.
There is a huge amount of knowledge on these boards and a huge willingness to help people, but there's no point in you asking again and again which areas have good schools, because it's not just as simple as that. The more information you can give the better people can advise you.