Be a loving family. It does not matter how much education is flying around, secure children will be the ones who are best off. Don't let achievement matter more than the fact you love them. Or let achievement matter more than doing other things that help you all mutually within the family.
Don't make them feel tested all the time. Just demonstrate a love of things: it could be cooking and reading cookery books; going to look at an art gallery; collecting plants and looking them up etc
At private schools the big thing is not money but that there is an expectation that it is normal to work hard and care about education. If some friends/contemporaries at a school where they are don't feel the same way, make sure they know it's OK to make these things matter and follow their own way.
Then what other posters said: read, read, read. Read to them for pleasure (if they enjoy it) even when they can read themselves. Go to the library every week to choose new books. Have meals together and talk. Talk about the news, or anything.
Don't allow mobiles/ipads/computers into bedrooms or at meals. Limit television.
When you talk, explain why you think what you do. Parents of children who become educated talk to children as people from when they are born. Invite relatives of different ages and talk to each other - not just have adults talking together in place, children talking together in another.
There are very educated people who are not rich: vicars, teachers, etc so it is not hopeless at all, even if money does make it easier to do nice things.