Where to move to in London with young kids

[undereyebags]

I know this has probably been done to death sorry!
Have 1m max max max budget. Would want to do work - not quite a proper renovation but more than happy to do kitchen, extension etc over time. Want a garden and prefer not to be 1930s suburb as they give me the shudders - though this is from past bad experience so perhaps if area is lively I could be persuaded.
2 pre schoolers so need to be in catchment for good state primary.
In an area with some community feel and a bit of soul - villagey if that is a word? And near green for children. Obviously needs to be safe area. Not asking much am I?!
Don't want to move out of London. We've thought about it and not ready. Plus both work so don't want commute to be too long - max hour door to door. Work near Bank/Barbican way. Happy to cycle/run to work too.
Currently looking at:
Crystal Palace
Alexandra Palace
Twickenham

Any other good areas you can recommend and why?

Thanks!!!

Ha! I'm with Albert. Because then you'd be in Kent/East Sussex/wherever. London is brilliant ta very much

be at London Bridge in under 40 minutes.

On a good day. On a typical day you'll have to leave an hour earlier than you really need to, just to ensure you get to work on time, and get home when it's dark. In June.

If ponies are so essential OPS DCs, she can move to Dulwich and have ponies and a riding school right on the doorstep, without any soul destroying commute to a rural hellhole satellite town with no facilities or spirit

I love London. I think the schools are great and there is a heap of stuff to do plus easy to get out to countryside. We are v active outdoors people so our kids will be forced to go on walks in the woods with us and sure we can get a dog in London!
Maybe in the future moving out would work but I'd just feel far too isolated and I wouldn't feel comfortable with the commute and being so far away. And not sure what would happen when school starts? I'd either have to leave work or try and get more work at home time somehow. I think we can get something decent with our budget so id rather stay than get a big executive home somewhere to rattle around on feeling lost. We did think about moving out but just not ready yet plus because we have a reasonable budget we thought we would be able to get a home somewhere still in the city we love - just not quite sure where yet!!

Have you looked at Sydenham, OP? You get quite a lot of house for your money, good schools, a couple of nice parks, z3 with overground and ELL, and the best restaurant in London according to trip advisor...

this house would put in .1m away from Ofsted Oustanding Haberdashers' Aske's Hatcham College... It has a primary school too and goes straight through from 4-18.

Camberwell! So often overlooked for some reason but it's great. Very friendly, super convenient for your work (could cycle in, or take bus, and be in inside 30 mins). Lots of lovely small restaurants/shops, and you are near East Dulwich if you want to be a bit more chi-chi, and Peckham. This one ticks most of your boxes for £850k and for an extra £45k you could get a4th bedroom in the loft: www.rightmove.co.uk/property-for-sale/property-40947399.html