Moving out of London - but where?!

[MyUserName1234]

DP and I have been talking about moving, as it feels about time to leave our rented 1 bedroom place (near London bridge) and move somewhere where we can raise a family.
We both need to commute to the centre (near the city and waterloo). We love where we currently live, short commute and lovely vibrant area. Though primary schools are good in the area, it seems like secondary schools are only an option if you can afford to go private, which we are unable to do. Hence our primary aim is to move somewhere with:
1 good secondary schools. Ideally non religious.
2 a vibrant atmosphere, we definitely prefer a city/town to countryside.
3 ideally less than 30 mins on the train
4 prefer to be north of London as our families live in the Midlands, though we wouldn't discount other places that fill the above criteria.

I know that being somewhere with good schools and good transport links is going to be pricey. We'd like to spend around 650k, but at a push could look to spend 700k-750k. 3 bedrooms minimum and some outdoor space.

Due to go to St Albans on Sunday for a look around, any other advice for places and areas would be appreciated!

Why secondary schools if you don't even have kids yet? [baffled face]

Teenagers can manage a much longer "commute" to a good school than a child can. You might have completely relocated back up north by then?

There's an interesting article in The Telegraph today about buying - it was recommending Northamptonshire but also flagging parts of London that are likely to rocket in value when Cross rail opens.

I think you need to think about how likely you are to visit family regularly when your kids are small. If you both travel home at least once a month then buying in South or South West London will be a real hassle and will add another hour to your journey.
You need to weigh up the frequency of your visits home versus your daily commute time/cost of housing instead.

It might sound unusual that we are exploring a lot of possibilities, but we want to make sure we do enough research. We know the area where we live, but unfortuantly the commutable places to London are a bit of a mystery to us. We are looking for an area where we can live comfortably for a long time! I appreciate no one can look into a crystal ball to tell us about schools in the future etc. If education wasnt an issue, we'd happily stay put

Ideally we dont want to fall in a trap of buying a place that doesnt meet our needs in the next 5-10 years.
I don't expect to find something that is perfect, I know there will be compromises, but I want to make said decision armed with knowledge!

We've been collating all the feedback and are considering SE London. Easy commute, which isn't so expensive as the places outside the m25. All the suggestions made have been really helpful!