To put my 2-pence worth in, Scotsnet always seems to have a rose-tinted view of London and the South-East in general.
While it’s true there are some nice places there it is also true there are a lot of places that make even the areas considered bad in Scotland look like paradise.
There are a lot of comments about places that are as similar to London as possible, only you can decide if that’s what you want but a change is not necessary a bad thing.
Your budget suggests if you stay in London you will not be living in an area that will be good for bringing up kids, will have to deal with issues that most here would struggle to even imagine.
That budget however will give you a much better lifestyle in Scotland, you won’t be the first person who has moved with no connections here and the areas/towns around Glasgow are reasonably diverse.
There is also a habit here of only suggesting one or two areas around Glasgow based on school performance, in reality there are loads of nice areas with good schools around, even the areas which are less desirable have better (and more importantly safer) schools than inner-city London states.
Good luck and really hope you are happy here.