It's good to have a plan for the next 16 years, but I don't know anyone that has not changed track in some way (school, job, house, marriage, etc) in such a long period of time. Don't bank on long term predictions!
There is a lot that can change, not just academic ability, at different ages - imagine a boy at all these ages: 2, 5, 9, 11, 13, 16 and 18!
You may find that the "one stop shop" school was great for your 5 year old but there are better fits for your 11 year old. Take care not to get locked into a school that won't support you moving but just as happy to kick you out when "brighter" kids turn up at key stages (aged 7, 8, 11, 13, 16).
As for the "private" question, you sound pretty die hard on that point.
For what it's worth I did a quick search on the DoE database for state primary schools within 1 mile of E14. There are several that have a very high cohort of children achieving a level 5 or above. Given they don't have academic selection that is (I suspect) easily as good as any prep school.
For example Bygrove Primary got 57% of pupils to level 5 and above and their "value add" scores are pretty good. There are a 5 or 6 others with similar outcomes. Statistics don't mean much, but have you actually visited these schools to dismiss them as possibilities?