Many of my family traditions are British. I am a third generation Australian on my mother's side and a fourth generation Australian on my father's side.
The Christmas tree and the presents under it come from Queen Victoria and Prince Albert. It was originally a borrowing of Albert's from his native land of Saxe-Coburg (now part of modern Germany). He grew up with this tradition and so passed it on to his wife and children. Then it spread from the royal family outward. People in Britain just loved the idea and took to it. Traditions of eating plum pudding and ham are probably much older.
The song Silent Night, a favorite of mine, dates back to Victorian times and I believe it originated in Austria. There is a lovely story set in December of 1914, close on a hundred years now. In the trenches of the Western Front there was an agreement not to fight during Christmas day unless fired upon. It was something both sides honored. Then the Germans began to sing Silent Night in German and the British troops opposite them began to sing the same song only in English. Gifts of food were exchanged between German and British soldiers and there were football games. The truce lasted from a day to a week, depending on the locale in the line. When it was over both sides started up the fighting and killing again. The military leaders on both sides made sure this truce would never occur again in the coming years of WW1. My grandfather fought on the Western Front during this most terrible of wars.
Personally I love to see at least one version of A Christmas Carol by Charles Dickens. I love the American cinema adaptation Scrooged but also have a fondness for the Black Adder salute as well as the Doctor Who tribute made a few years ago. I once saw a live stage play version of A Christmas Carol and have Dickens' original written story along with his other Christmas tales.
There are of course traditions that are completely Australian which make Christmas something special. There is the beach and the BBQ. I like seeing people having fun in the sun on this most joyous time. Ha! I like the beach and the BBQ also for my family and yours truly. Merry Christmas!