I live in the kind of place you describe. It's Dalgety Bay, near Edinburgh.
For £1.2M here, you would get an enormous 5/6 bed house with a swimming pool and a sea view. In fact you'd possibly have change. Have a look on Google maps, at a street called Donibristle Gardens.
We have 2 excellent Primary schools, and a brand new state of the art High School is currently being built to replace the existing High School. We have a couple of excellent restaurants, about 5 take-aways, Asda, Tesco, all the amenities you'd need. It's very family friendly, with regular Gala's for the children. We have 5 lovely beaches.
Also, within very easy reach is South Queensferry, which is also on the seafront, with a long cobbled street lined with bars and restaurants.
There are lots of other villages towns, and up here each town has it's own Gala day in the summer, and Highland games days - brilliant for kids.
The train into Edinburgh is about 20 minutes, and of course you have everything you could possibly need there. Lots for kids like the Science Museum, regular museums, the festival every August.
Closer to home is Dunfermline, with everything you'd need for kids, like bowling alley, cinema, swimming, loads of child friendly restaurants.
We don't have the immigration problems that you have down South. Also, if your kids go to Uni, it is FREE up here. We moved here from England in 2003, and both of my kids had free Uni - absolute huge plus imo!
Hospitals are much better up here. Never long waits. I would never move back to England.