Don’t be seduced by what you can get for your money. In reality it could become a gilded cage and feeling stuck in an area which is a completely different culture is a shock to the system.
If you really want to live there I would suggest renting for a year and rent your own current house out before actually buying.
I live in the very outskirts of North London and we feel very safe.
We actually have left our front door open, (it got warped in the hot weather a couple of summers ago). We were confident that no one would enter.
We do live in an area (almost a hamlet) where no one quite knows that we exist.
There are other areas of London or Home Counties borders which are much safer than areas of south London.
I have certainly noticed how much easier and cheaper it has been that teens have access to the tube and to London.
Friends who moved out to the countryside spent years being a taxi service to their children who have now all upped and left for uni and are not likely to return because of job prospects.
I think you need to think long term not just the schooling years
Is there lots of job prospects for children when they are adults. If your children go to uni what would make them return.
I know everyone says that there is good transport links to London but the time and cost should be taken into consideration.
Personally if the only reason you are leaving your area is because of safety fears and you have picked Norfolk because housing is cheap then I think it is throwing the baby out with the bath water.
Move to another area of London or Home Counties.
You might not get as much for your money but your children will thank you in the long run.