Australian family with British parents & grandparents

Hello

My wife and I and our two children would like to go to the UK to live for 12 months. The purpose of our visit will be to spend time with our relatives and to travel around the UK and some of Europe.

In order to survive for 12 months my wife and I both aim to work for approximately 9 months of the year. We will be selling our house here in Australia and using some of this money to support ourselves when not working.

Both my wife and my parents were British citizens as our grandparents.

As we live in a commonwealth country (Australia) and our parents and grandparents were British does this mean we can (or already are?) British citizens and/or get British Passports? And if we can get British Passports does that mean that we are British citizens and can therefore work in the UK, or do we still need to get visas to work there?

The second issue is the kids, as they were both born in Australia to us (Australian citizens) will we be able to enrol them in school in the UK or will they need a visa as well?

I have tried looking on the UK Border Agency website as well as the British High Commission website but am unsure what the best way for us to enter the country will be as there is confusing information on these sites.

Thanks very much for your help

When and where were you and your wife born?
Were both your parents and your wife's parents born in the UK?
Are your and your wife's parents married?
How old are your children?