The idea that the United Kingdom should try and rebuild closer ties with Canada, Australia and New Zealand raises its head from time to time. Obviously we’re close friends, with ties of history, language and culture, and there’s nothing wrong with reinforcing old friendships. But thanks to Brexit, we’re hearing a bit more about this kind of thing than usual — with a focus on some kind of economic and geopolitical partnership.

So is there a business case for CANZUK as a primary relationship for any of these four countries? Let’s look at where our potential partners currently sell goods and services.

In the United Kingdom, nearly half of our exports go to the rest of the EU. When you add EFTA members in, a majority goes to countries in or partly in the single market. By far our largest non-European partner is the United States. China and the Gulf Co-operation Council states both come in ahead of CANZUK. You might try and argue that we’ve had a lot of trade diversion to the rest of Europe. But even if you doubled our trade with Canada, Australia and New Zealand, it’s never going to be anywhere near enough to make up for the hit to our European trade. We are a Euro-Atlantic economy.

In Canada’s case, it’s quite obvious that nothing and no-one could match the scale of US trade. It’s next door, it’s huge and it’s economically fairly integrated. Again, China and the EU-27 both come in ahead of CANZUK. Again, there’s no way CANZUK could even come close to matching trade with the neighbours.

A clear majority of Australia’s exports go to east Asia, with the developed English-speaking world clocking in at about 10%. CANZUK would theoretically be the fourth-largest destination for exports, but over half of them go to New Zealand. (Let’s also note that Australia and New Zealand already have a free trade agreement.) Australia trades mostly with its neighbours and within its geographical region.

New Zealand is the only CANZUK country where CANZUK would be the top recipient of exports (or even in the top three). But that’s overwhelmingly down to Australia, where 17% of New Zealand’s exports go. The UK makes up 3.4%. (Incidentally, the EU-27 accounts for about twice that.) Again, New Zealand is mainly an Asia-Pacific economy.

So all four of our prospective partners show the usual truth in trade: countries tend to sell to their neighbours. The UK, Canada, Australia and New Zealand are already mature, developed economies, so any idea that their vast growth potential could make up for diversion from elsewhere doesn’t stack up. There is no sensible case for CANZUK as a main economic bloc for any of its members.

But CANZUK has been sold as a geopolitical partnership, not just (or even mainly) an economic one. Do the defence and security arguments stack up any better? Clearly the four countries spend a large amount on defence between them — over $96 billion, though nearly 60% of that is spent by the UK. We have served together in many conflicts. Australia and New Zealand are committed to each other through ANZUS. Canada and the UK are allied through NATO.

But again, look at members’ defence strategies. The four countries share two main things: a predominant focus on their own regions and a critical dependence on the US. Our most important joint defence endeavour is the Five Eyes, where the US is the most powerful member. Only the UK even aspires to have a global reach in its own right. Our Strategic Defence and Security Review cited our military and intelligence’s ability to ‘project our power globally, and … fight and work alongside our close allies, including the US and France, to deter or defeat our adversaries.’ Note the US and France are the two main allies cited. It is abundantly clear that the UK’s main defence commitment lies in NATO.

Australia’s Defence White Paper from last year is clear. Its priority is to ensure an independent ability ‘to defend Australia and protect our interests in our immediate region,’ and then to ‘enhance Australia’s ability to contribute to global coalition operations.’ Its two principal allies are the United States and New Zealand. Canada’s key roles are ‘defending Canada,’ ‘defending North America — in partnership with the United States’ and then ‘contributing to international peace and security.’ New Zealand’s focus includes the need to ‘defend New Zealand’s sovereign territory’, ‘meet New Zealand’s commitment as an ally of Australia’ and ‘contribute to, and where necessary lead, operations in the South Pacific’.

Granted, the UK, Australia, New Zealand, Malaysia and Singapore have one joint security commitment. They have agreed to consult on responding to a threat to the latter two countries. But the Five Power Defence Arrangements aren’t a collective security agreement. They stem from a UK withdrawal from commitments east of Suez in 1968–71, not a willingness to take on new ones.

The FPDAs are generally agreed to contribute to security. But does anyone believe the UK and Canada could possibly defend states in the Pacific in an existential crisis without the US? Would Australia and New Zealand be in a position to assist in Europe if the roles were reversed? That may be a remote prospect, but a true collective security commitment requires the answer to be ‘yes’. I don’t think anyone actually believes that would be the answer without the Americans. So what, meaningfully, are we going to do together in the field of security and defence on our own?

There’s no decent case for making an economic priority of CANZUK. There’s no real defence or security case for it either. We’re all liberal democracies with similar positions on global issues, but we can already co-ordinate our foreign policy as and when we want. No doubt we could bring in freedom of movement between our countries if we particularly wanted, though it’s hard to see that as practically transformative. But in the end, this is about sentiment.

If ever the UK needed to be frank about its role in the world, the time is now. Brexit is going to be damaging anyway: if we get it wrong, it could be catastrophic. Our priorities are to minimise the damage to our relations with our nearest neighbours, try to keep the transatlantic alliance in one piece and develop economic ties where they will do most good.

Whether we’re ‘more like’ continental Europe or mainly-anglophone-developed-democracies-but-not-the-US is subjective and highly politicised. Much of the argument boils down to rival sentiments. But our trading patterns, principal threats and security priorities aren’t sentimental. And an economic, foreign or defence policy governed by sentiment would be doomed to failure.