| It doesn't stop|
at the water's edge
CANZUK (pronounced /kæn‘zʊʔk/, CAN-zuk) is the political philosophy of economic integration of the Anglosphere or the White Commonwealth. The name comes from the abbreviation of the countries in question; Canada, Australia, New Zealand and the United Kingdom, hence why it is always written in all capitals. The idea is that these four countries should work together and allow near-complete freedom of capital, goods and services, but principally freedom of movement between the four countries. The phase CANZUK come from a book written in 2016 by the anglophile American writer James Bennett called A Time for Audacity. 
It is often used as a counter against regional integration in terms of the European Union and the United Kingdom. With the thinking being, 'why should we discriminate against Australians and New Zealanders who are our “kith and kin”, compared to those French, German and Polish foreigners?" So naturally, it is Eurosceptic. The organisation that promotes this philosophy is CANZUK International, formerly known as the Commonwealth Freedom of Movement Organisation. Supporters of CANZUK are often known simply as "CANZUKer" in their own jargon.
While it claims to be non-partisan it is a deeply conservative philosophy, with all the people spouting support for it being conservatives. Notable supporters included New Zealand-born British writer Andrew Lilico, Canadian Tory politician and current Official Opposition Critic for Foreign Affairs Erin O'Toole and Australian Liberal Senator James Paterson. It should also be pointed out that the chaps who started the idea of CANZUK, James Skinner of CANZUK International who currently works as a paralegal in British Columbia, is a former Vice-Chairman of Conservative Youth. and James Bennett is a fellow of the conservative think tank the Hudson Institute.
CANZUK has been pushed by Atlas Network connected Thatcherite think tank Adam Smith Institute.  At the end of 2018 another connected think tank also supported CANZUK, the libertarian Institute of Economic Affairs. 
Notable sympathisers to CANZUK are the former prime ministers of Australia John Howard and British-born Tony Abbott, former Australian High Commissioner to the UK [Ambassador] Alexander Downer,  British historian Andrew Roberts, British prime minister Boris Johnson and former Canadian prime minister Stephen Harper, plus current Canadian Tory leader Andrew Scheer.
The initial idea was that the four countries would allow the current visa requirements for Australians and New Zealanders to live and work in each other's country under the Closer Economic Relations policy of the Trans-Tasman Travel Agreement, to be expanded to include the UK and Canada. However, since the Brexit vote, it has expanded to include trade and economic links between the four countries.
"Kith and kin"
CANZUKers say that the reason for linking the four counties is that they all have Queen Elizabeth II as their monarch, similar parliamentary systems, legal systems of common law and trade position of being free-market liberals and the fact they all speak the same language. They tend to emphasize the “Britishness” between the nations, using the term “kith and kin” to talk about their "people".
They conveniently ignore that all have republican movements, which are especially strong in Australia.  Although they have parliamentary systems; the Beehive in Wellington is unicameral, Australia and Canada are confederal, and Australia and New Zealand use voting systems found in Germany and Ireland. With regards to legal matters, both Scotland and Quebec have a version of civil law for their courts. Historically, all were but particularly both Canada and New Zealand were notoriously protectionist, with their monetarist trade practices only came about in the 1980s under Brian Mulroney and Roger Douglas.
Ask why CANZUKers don’t want to include places like Malaysia, Singapore, India and the United States. They claim the CANZUK countries are: “they are highly economically developed countries, with sustainable economic growth, positive human rights records and a shared historical and cultural bond through a democratic monarchy.”  Plus, also if the United States was in, they would dominate the group instead of the British.
Many CANZUKers are militarily obsessed, and often use the phrase “Five Eyes” as another term for CANZUK, which refers to the Five Eyes intelligence system of links between the police forces and intelligence services of Canada, Australia, New Zealand, the United Kingdom and often conveniently forgetting the elephant in the room, the United States. Five Eyes itself is based on the agreement during World War II, when Churchill and Roosevelt agreed not to spy on each other and coordinate matters on intelligence. Many CANZUKers laud any military coordination between those four countries; such as proposals for suggesting co-operation in naval matters in East Asia between the UK, Australia and New Zealand as a way to beef up British military support.
However, CANZUKers conveniently forget that much of the British international military co-operation is with NATO, of which the UK and Canada are members and both Australia and New Zealand are contact countries. It should be noted that other contact countries include Japan, Afghanistan and Columbia. But then again, being in NATO did not stop the U.S. and Canada from creating NORAD.
CANZUKers also conveniently overlook that not all conflicts near and far were supported by all other nations, such as the Iraq War which was boycotted by the Canadians and the Vietnam War which was not taken up by the British and the Canadians. But then again, just because any two countries are in the same alliance does not mean they will share the same military engagements.
Further reading & information
- Kenny, Michael, Pearce, Nick (2018) - Shadows of Empire: The Anglosphere in British Politics, Wiley ISBN 9781509516612
- Murphy, Philip (2018) - The Empire's New Clothes: The Myth of the Commonwealth, C. Hurst & Company (Publishers) Limited, ISBN 9781849049467
- Bell, Duncan, Vuectic, Srdjan - Brexit, CANZUK, and the Legacy of Empire
- The CANZUK Union Explained - Explaining Brexit - from YouTuber, TLDR News
- Bennett, James C, Time For Audacity: How Brexit Has Created The CANZUK Option
- Bennett, James C, "Brexit boosts 'CANZUK' replacement for European Union: Column" USA Today
- Erin O'Toole Talks CANZUK with CANZUK International, YouTube
- Senator Paterson calls for a CANZUK agreement in the Senate, YouTube
- James Skinner - LinkedIn
- Kilcoyne, Matt, "Our CANZUK friends should be welcome in post-Brexit Britain" City AM
- Powell, Jack, "A “Global Britain” must embrace migration" Institute of Economic Affairs
- Bourke, Latika, "Alexander Downer flags 'freer movement' for Australians emigrating to Britain", Sydney Morning Herald
- Australian Republican Movement
- Frequently Asked Questions, CANZUK International.
- Archive on 4 - Return of the Anglosphere BBC Radio 4
- Canzuk Defense opportunities in 2019, Daily Globe
- See the Wikipedia article on Foreign relations of NATO § Global NATO.