At the heart of the Conservative Party’s leadership turmoil is a particular vision of what Brexit is for. For many Tories, the Irish backstop and Theresa May’s talks with Labour are toxic for the same reason: they threaten to lock the UK into the customs union, giving up what some have called the “great prize” of Brexit: an independent trade policy.

In these circles, the vision of a swashbuckling Global Britain, unencumbered by Europe, has become an article of faith. Britain can strike better, faster trade agreements and enormously boost trade with the rest of the world once it escapes the customs union – or so the argument goes.

The reality is that “independent trade policy” is not a magical phrase that can turn Britain into an influential nation in global trade. In practice, as our new research at Global Future shows, it means leaving the world’s most advanced free trade area in pursuit of new agreements that will deliver less trade on worse terms.

Reporting on most studies of the economic impacts of Brexit has sensibly focused on GDP and incomes. But there will also be a sizeable reduction in trade – one that new trade deals will almost certainly not replace.

Estimates of lost trade with the EU range from £37bn to £150bn per year, even for future relationships based on May’s Chequers model. Under a “Canada-style” free trade agreement, the hit to trade volumes could be as high as £279bn every year, affecting both imports and exports.

It’s desperately unlikely that replacement trade deals will be able to compensate for this blow. Our analysis of government figures shows that signing free trade agreements with 17 countries – including the biggest fish, United States, China and India – would compensate less than two-thirds of trade lost with the EU. If the future relationship was a Canada-style deal, the trade created by new agreements would be less than 20 per cent of the losses. The National Institute of Economic and Social Research, similarly, found that trade deals with all of the Anglosphere and BRIICS (Brazil, Russia, India, Indonesia, China and South Africa) countries could replace only about a fifth of that lost with the EU.

But the real worry about an independent trade policy is what the government will have to give away to win these inadequate replacement deals. Our analysis of academic literature found five factors that determine a country’s bargaining power in trade negotiations: market size, existing trade dependence, current market access, their best alternative to an agreement, and their ability to make offers outside the sphere of trade.

In every one, the UK is a less attractive and less influential partner than the EU. Our market size, naturally, is far smaller, whether measured by GDP or foreign investment volumes. Most potential partner countries trade much more with the rest of Europe than with Britain. The UK will already be more open to international trade – with tariffs the same or lower than the EU’s, and lower non-tariff barriers thanks to its lighter regulatory approach – which means we have less to offer. Our outside option will be non-existent, with no other trade deals in place and a post-Brexit prime minister so visibly desperate to seal a deal and “make a success” of Brexit that they can’t walk away.

That doesn’t mean nobody will be interested in striking trade deals with the UK. Some partners, like Australia and New Zealand, will probably seek to open negotiations almost immediately after Brexit. But both of those countries have already started negotiations with the EU, whose markets they will rightly prioritise as a much bigger prize.

The upshot is that potential partners, particularly trade superpowers like the US and China, will drive a hard bargain. America’s stated priorities for future talks, though couched in the dry language of trade negotiators, paint a vivid picture. They include aims to change regulations to “foster innovation” in medicines – code for higher drug prices, which the US says pharmaceutical companies need to fund research – and abolish many geographical indications that protect goods like Stilton. That’s in addition to the widely-discussed changes to food safety restrictions, where the US feels that rules against hormone injection of beef cattle and mass use of antibiotics are unjustified.

Outside trade and regulation, some in the British government – including the country’s most senior civil servant, Mark Sedwill – have been eager to use foreign and security policy to help win trade agreements. That raises the spectre of concessions in foreign policy being used to win trade deals with China. After last month’s Huawei uproar, China’s ambassador to the UK wrote an opinion piece using language directly linking security decisions like this to trade partnerships, saying that “the last thing China expects from a truly open and fair ‘global Britain’ is a playing field that is not level”.

The fact is that post-Brexit Britain will be in an extremely weak bargaining position. The government’s ability to negotiate ambitious new trade deals – especially ones including services, the competitive advantage of the British economy – will be very limited. We will have to give away a lot to strike new agreements that won’t come close to replacing the trade we lose with Europe.

This is the great prize that champions of an independent trade policy are pursuing, and that has shaped the Tories’ catastrophic approach to Brexit negotiations. When its advocates say that Britain will be able to negotiate trade deals faster and better than the EU does, they are concealing the truth that we can do that only by making sweeping concessions, both in trade and beyond it.

The outcome of winning back an independent trade policy is not the rebirth of Britain as a global trading nation. It’s exactly the opposite: a future in which we have less bargaining sway, lower regulatory standards, and – most perversely of all – do less trade.

Fergus Peace is a researcher at think tank Global Future.