Where to look in London?

[Coronet08]

Merry Christmas everyone!
After some advise from a brilliant hive mind, as we are looking to upgrade our 2 bed flat in North London to a 4/5 bed house anywhere in zones 1-4. We have 2 small children now, so really need more space and (state) schools are key!
Our budget would stretch to £1.3m but probably not beyond, and where we live now we would not be able to afford a decent family home for this, despite both of us being high earners.
Not looking to move for secondary schools, so both excellent primary and secondary need to be close by (we qualify for Catholic schools, too). Also not looking for a project, so the budget is for a "done up" property really.
Good transport links are vital (tube/Elizabeth line), as both me and DH will need to travel to work several days a week.
So far we are looking at Ealing and maybe Muswell Hill (nearer to East Finchley station). Any other areas we are missing where one can bag £1.3m house with 4/5 beds?
Thank you so much in advance!!

Wherever you are thinking of, I would look carefully at the flood risk and try to buy somewhere above the flood plain. Don't rely on the government to sort out flood defences before things go tits up.

I thought for that area you looking nearer 1.5/1.6 and it’s a good walk to either tube from there