As a Canadian, this is a pipedream, at least for Canada
Canada and Australia have generally similar economies, both dependent on trading in raw materials, both have seen manufacturing drop within our respective countries. A union between both provides no benefits economically as we are more competitors than natural trading partners. Canada is dependent on the US for trade, and no matter which president in power the US would likely take offense to Canada forming a union with other countries that is a competitor to the US for political power, military power and economic power. The same reasoning for the UK to leave the EU would apply for Canada and any union with the UK/Australia. Given the small size of the union, 4 countries and the much larger power level of the UK, it would dominate the union far more than any country in the EU did
For Australia, it is economically dependent on China, with only India or the US being able to replace Chinese markets for its exports The UK certainly can not find a use for the raw materials from Canada or Australia. Security wise, the UK is going to decline over the next 30 years, Canada is not going to get any better (and has no need to), forming a security union would benefit Australia, but it would not get any from Canada or the UK (to far away, and too large)
Overall just a dream from the UK and people who dream of the British Empire. Few in Canada care about the UK (at least among those younger than 60, as the US is far more important in most peoples lives