It makes almost no sense for the Brexit debacle to have come down to the issue of an 'independent British trade policy'. Trade was not a central issue at the referendum and remains wildly misunderstood by public and politicians alike. But we are where we are. If we end up crashing out by accident, or the May government tears itself apart, it will be on the pretext that significant numbers of Tory MPs want that independent trade policy and cannot stomach the restrictions that a customs union would put on Britain’s freedom over trade.

It’s hard to know where to start with trying to dismantle the trade illusion, so long is the shadow it casts over almost the entire Brexit debate. But it stands not on facts but on belief, and especially the belief that Britain is bigger, more important and therefore better able to strike trade deals to its advantage than is actually the case.

It is a truism among a certain sort of Leaver that Britain is, economically, a bit of a catch – if only we sold ourselves better. If we only showed a bit more confidence we could do so much better for ourselves. Rule Britannia and all that. Even Cabinet ministers – who really should know better – go in for this stuff. Even in private.

But as every short man secretly knows, thinking you’re a giant doesn’t make you any taller.

In trade, size matters. Bigger trading partners are better able to set terms for smaller ones. In the words of Dennis Novy of the Warwick University economics department, in trade talks you’re either the bully or you’re bullied. As part of the EU, Britain was one of the bullies of global trade. Outside, not so much.

Yes, we have a population of 70 million and GDP of almost $3 trillion. But for comparison, the EU (including the UK) and US both have GDP of more than $19 trillion and hundreds of millions of consumers; Chinese GDP is somewhere over $12 trillion. India’s economy will soon be bigger than ours, if it isn’t already.

Leaving the EU will reduce the trade we do with the EU: there is no way that leaving a free trade agreement makes it easier to trade with its remaining members. The Brexiteer theory is that we will more than make up for any such loss with trade deals elsewhere. The numbers behind that idea are highly contestable, but the fundamental concepts of 'free trade' are even more important here.

The very idea of free trade is largely misrepresented in Brexit discourse. Some Brexiteers talk of Brexit allowing the UK to trade freely with the world 'on WTO terms' as if that meant an end to all tariffs and regulation. That’s not utterly absurd: it could mean using our new freedom to adopt a position of unilateral free trade, by simply scrapping all import tariffs. This is the sort of position that sounds good in the offices of London think-tanks and newspapers, but is to all intents and purposes politically impossible since it would mean the effective end of UK manufacturing and farming.

So 'free trade' would actually mean trade agreements. Such agreements aren’t much about tariffs any more: globally, tariffs are fairly low overall, with the exception of sensitive stuff like food. What FTAs are really about are standards: parties agree to allow the trade of goods and services as long as those products meet certain, mutually-agreed rules.

And who ensures those rules are upheld? There are two mechanisms: state-to-state negotiation overseen by the WTO, or a bespoke arbitration body overseeing the FTA. In a sense, the distinction is irrelevant here: in both cases a country that is party to a free trade deal must sometimes accept decisions on trade that are not wholly made by the elected leaders of that country. 'Free trade' means giving up some control and the deeper your agreement, the more control you cede.

How would this look and feel in reality? How would Britain fare as it exercised its newfound 'freedom' via its independent trade policy?

Let’s start with America, since that’s where many Brexiteers look when they talk about trade. That’s quite reasonable: it’s still the world’s No. 1 economy and Britain’s strategic ally, after all.

Any trade talks with the US would be unequal, possibly painfully so. Some of that is about numbers: the US is just a lot bigger than the UK, and has less to gain from a deal.

There’s also an inequality of urgency. Outside the EU, the UK will need a trade deal with the US very badly, for both political and economic reasons. Many Brexiteers have admitted as much, at least tacitly. UK-US talks would be a negotiation between a large player who didn’t need a deal and a smaller player who not only needs to do a deal, but who had publicly stated that desire. How do you think such a negotiation would go?

Of course, some people talking about this issue like to mention Donald Trump, who has indeed said some positive-sounding things about a possible UK-US trade deal. But does he mean it? Would an actively protectionist – and personally mercurial – US president really seek to spend political capital striking a trade deal which was advantageous to the UK? (And let’s not talk about Congress, which has a say here too.)

Oddly, the same people who dismissed Barack Obama’s 'back of the queue' warning as empty political game-playing are rushing to take Donald Trump at face value over trade.

But let’s pretend the US really is keen to strike a deal. What would it want? The shopping list would very likely include US-acceptable standards on food safety, labelling, environmental protection and maybe data handling and better access to NHS procurement systems for US pharmaceutical firms.

Perhaps you think the US would approach trade negotiations focused on anything other than its own national interest. Perhaps you think any US administration would cut Britain a bit of slack in trade talks because of our shared history and culture. Perhaps you think a British government could win popular British consent for hormone-treated beef, GM food and a role for US business in the NHS. If so I have a bridge over the English Channel to sell you.

A glance at a recent US Trade Representative paper setting out US negotiating objectives also suggests another potential condition of any such deal. In any trade deal with Britain, the US would want the option to 'take appropriate action if the UK negotiates a free trade agreement with a non-market country'. In other words, if you want to deal with us, don’t do a deal with China too.

The bottom line is that to strike a free trade deal with the US, Britain would have to accept rules and constraints. Many of those rules might well be uncomfortable for British voters. Perhaps even more fundamentally, these rules would not be written by British politicians and British politicians would not have complete control over them.

What about China though? It’s the future, right? Maybe we could still somehow manage to negotiate a deep FTA with the world’s No. 2 economy? It is of course possible, but again, there would be a price to pay, and a price measured not just in control over economic rules.

China isn’t just a rising economic power, it is a rising strategic power. Chinese trade and investment are not just factors of economic interest, so any UK trade deal with China would have a strategic dimension. In exchange for favourable trade terms, we could have to, for instance, agree to support the Belt and Road initiative that is spreading Chinese infrastructure across half the world. Italy did last month, causing deep concern that Chinese money is undermining EU unity.

Buccaneering Brexiteers keen to trade with China should read this report by the Centre for New American Security, a bipartisan Washington think-tank. Its first observation about the Belt and Road is that it sometimes leads to the 'erosion of national sovereignty: Beijing has obtained control over select infrastructure projects through equity arrangements, long-term leases, or multi-decade operating contracts.'

Using a new independent trade policy to trade with China might be lucrative for Brexit Britain, but it would far from free. The price could be strategic, and might well raise some fundamental questions about the future of the West and Britain’s place in it.

The last of the big prizes in trade is India, often cited by buccaneers as a fast-growing economy where Britain’s historic ties make a trade deal feasible and attractive. Successive British prime ministers have made regular trips to India talking up such prospects.

But again, betting independent Britain’s future prosperity on an FTA with India is a plan that deserves close scrutiny of three significant aspects.

First, don’t hold your breath. India really doesn’t rush into trade deals. EU-India trade talks started in 2007 and are still going nowhere. To quote Kevin Rudd of Australia, writing last month:

'India’s trade and commerce bureaucracy is the most mercantilist and outright protectionist in the world. They virtually single-handedly sank the Doha round in 2009. In the same year, as prime minister of Australia, I launched a free-trade negotiation with Delhi. But a decade later, those negotiations remain at a standstill.'

(If Rudd is too left-wing for your taste, try this fine piece from the swashbuckling Institute for Economic Affairs, which is equally gloomy about any UK-India deal.)

Second, if you think Britain’s 'shared history' with India will be an advantage in trade relations, I suggest you read more books and maybe visit modern India, a country to which Britain is of fast-waning relevance.

Third, even if you can get past the bureaucratic inertia and the history, India too would have its price. The starting point for (very, very long) UK-India trade talks would be a significant relaxation of UK immigration restrictions on Indian nationals.

Perhaps you’re relaxed about that, as I am: a lot of Brexiteers have a long and honourable record of arguing for easier migration to the UK from countries such as India. But think about what it would mean if Britain agreed to ease its immigration rules for India as part of its new independent trade policy.

We would have left the EU because we did not want to accept the constraints it placed on UK immigration policy, in order to pursue a future where we struck an agreement that put constraints on UK immigration policy as the price of trading more freely with India

To be clear, I see nothing inherently wrong with that outcome: I’m positive about immigration and I accept that free trade deals mean compromises on domestic policy. But I struggle to see how that outcome is consistent with the alleged British demand to 'take back control'.

Of course, that’s because the very concepts of 'control' and 'freedom' on which so much of the Brexit case was built are simply impossible to reconcile with the reality of a globalised economy and Britain’s part in it. Some of the people who use those words to win votes and political advantage understand this perfectly well but do it anyway; others just don’t understand the basic facts. I honestly don’t know which group is worse. There is also something distasteful about people who won a referendum by talking about immigration now insisting that the whole thing was actually always about trade.

Yet here we are, a nation adrift. Our future hangs in the balance in part because a significant number of our elected representatives say they cannot compromise on their demand for Britain to exercise complete freedom over trade.

In fact, Brexiteers should hope they never get their wish. An independent British trade policy would be a slow-motion national humiliation that would once and for all shatter the 18th century version of sovereignty that sustains Brexit, and brutally acquaint the British polity with the reality of economic sovereignty in the 21st.

Brexit is not quite yet a Suez moment that forces the country to accept our actual place in the world, but the painful business of trying to implement that 'independent trade policy' could finally strip away the lingering fantasies that underpin this project. Another historical parallel might be even more pertinent: Brexit Britain’s experience as the weaker party in trade talks with the big powers of world trade might feel like going cap in hand to the IMF in 1976.

By the same token, perhaps Remainers taking the long view should actually want Britain to be 'free' to conduct its own trade policy. An exit that constrains that 'freedom' will only nourish a Brexiteer narrative of dream denied. The failures and disappointments of life outside the EU could forever be blamed on a customs union’s constraints on British freedom over trade, that stop this great nation (re)achieving its wave-ruling potential.

Any alternative form of exit would be deeply painful, but might just deliver one traumatic benefit: a head-on collision with the unforgiving reality of modern trade might be the only way to reconcile Britain to its true standing in the world economy. An acceptance that must eventually lead us back to membership of one of the superpowers of world trade, the free-trade agreement known as the European Union.