I think you are generalising a little bit too much. I am southern British, and whereas I conclude that northern British and Australians are generally pretty friendly and outgoing, I too make an effort to be the same, and have met plenty of people in southern Britain who are extroverted and make everyone feel welcome.
I think Australians come across as cheerful, chatty and open to strangers is due to the climate: warm and hot sunshine are definitely conductive to people being easygoing and joyful. Britain being a bit rainier and colder would curtail this a touch, but warm cafes and pubs in any British city, on a winter's day can be very welcoming, and I wouldn't want to be in Darwin when it gets really humid, and people 'go troppo!'
It could also have something todo with southern British people working hard and living in a fast pace of life. That means we tend to come across as not having much time for people, but it depends where you go. I was strolling around the Harringey 'ladder' on Saturday afternoon, and people were out and about, chatting to their neighbours in their front gardens. Go to somewhere like Bristol or Brighton, and people there are down-to-earth and broad minded too.
To explain the general Australian pre-disposition to cheerful bonhomie, you have to also look at the history. People mostly descended from convicts and imigrants, meaning that communities were close-knit and people looked after eachother. They also had the resources of a whole vast country to exploit, so that probably helped to foster a feeling of abundance and being provided for.
Finally, Australians classed themselves as a 'new world' nation fostering themselves in modern and dynamic ways, which bred a pioneering and go-ahead spirit among them and their collective psyche. What you need to remember though is that Britain also suffers from the colonial guilt born of our forefathers mistreating people in our possessions, so we may be reluctant to be patriotic and celebrate our history; but on the flip side, we are at the forefront of every trend in sociology, economics, art, leisure, sport and technology, which also perpetuates a go-ahead spirit in us.
Generally, Australians are cheerful, extrovert, welcoming, relaxed, forward thinking and broad-minded, but can also be brash and in certain quarters, there is a racism boiling away under the surface. British can be cold, pessimistic, hassled, reserved and narrow-minded in certain quarters, but we can also be cutting edge, creative, world-class, welcoming, jolly, helpful, honest and stylish.
There are bad and good elements in both countries; it just depends on where you go and who you meet.