Some leave voters hoped for control over immigration. Others expected a budget dividend for the NHS. But for many Tory MPs, Brexit’s most cherished prize was a rather more obscure benefit: restoration of an independent seat at the World Trade Organization, representing freedom to strike bilateral trade deals. No one is more excited about that prospect than Liam Fox, the international trade secretary. He could hardly conceal his impatience in a speech on Wednesday extolling the virtues of the WTO. He urged an audience of business leaders to pay more attention to the organisation. Implicit in that message is a complaint that the UK’s role in EU institutions has monopolised economic debate.

But access to European markets, integration in European supply chains and influence over EU rules cannot be dismissed as second-tier concerns. Most serious efforts to model Brexit show a substantial cost from quitting the single market and customs union. The idea that Britain can simply drop its existing arrangements and trade according to “WTO rules” is a fantasy advanced by hard Brexiters who either deny the damage that shock would inflict or relish it as purgative exposure to uncompromising global market forces.

There are reasons that no developed country in the world relies on the WTO as a framework for its global trade. The organisation sets common denominator terms of fair practice but that system is not sophisticated enough to obviate the need for deals between members. Negotiating those deals is never easy or quick. The current trade row between Beijing and Washington is a case in point. The world’s two largest economies are supposed to be finalising a bilateral accord, with China’s vice premier Liu He due to visit the US on Friday. But last week Donald Trump complained on Twitter that progress was too slow and threatened to increase tariffs from 10% to 25% on goods worth $200bn. The order to enact that hike has been filed. The White House accuses Beijing of reneging on commitments already made.

There is more to the clash than just trade; the US and China are engaged in a long-term rivalry for global leadership. Ramping up tough rhetoric is also a routine part of Mr Trump’s domestic political showmanship. However, one feature of the Sino-US deal that Brexiters like Dr Fox should note with alarm is a bespoke dispute resolution procedure. If completed, that feature would bypass the WTO – an outcome consistent with the US president’s loathing of multilateral institutions that might constrain his actions. Theresa May could try asking Mr Trump to be more respectful of international rules when he visits London next month, but she wouldn’t get far. Besides, she fears alienating the man who can bestow promises of a “special” post-Brexit deal with the UK. But the idea that Washington, under any administration, would do favours for Britain in international trade talks is one of Brexit’s wilder delusions. It is an arena where cold realpolitik is paramount and size matters. China is currently testing the limits of its leverage as an emerging superpower.

It is a simple fact of geography and scale that the UK cannot compete in that league. In equivalent talks it would have terms dictated in much the way that Brussels, representing the collective mass of 27 countries, has been able to dictate terms of withdrawal from the EU. The same would be true if the UK sought to negotiate its way back to single market access from a base of WTO rules. A painful lesson from Brexit is that UK has more influence as a big player in a European bloc than as medium-sized player alone in the world. The idea that it is worth swapping a seat at the EU’s top table in exchange for a seat at the WTO is one of the Brexiters’ most fraudulent claims. It is a bad deal that promises worse deals to come.