The idea of buccaneer Britain trading freely outside the EU is a fantasy

Brexit, they say, would free Britain to sign bilateral agreements with the rising stars of Brazil, Russia, India and China, or with the "Anglosphere" of Australia, New Zealand and North America, without having to reach a consensus of 27 EU member states. They point out that the rest of the world is going faster than the EU, offering opportunities which would make up for any forgone trade with Europe. And therefore, they argue, Brexit would therefore boost the British economy in the long term – especially if you throw in some deregulation to boot.

But this commonplace view is wrong, and there are three reasons why.

The first is distance. Imagine if all of Britain's trade agreements were suddenly erased from history, and we had to restart our negotiations from scratch. Our first priority would be to reduce the cost of trade with big, nearby economies. Trade diminishes quite rapidly with distance: half of Britain’s exports go to the EU, which makes up a fifth of the world economy. Meanwhile, the non-European members of the OECD – although they comprise a third of the global economy – only buy a quarter of Britain’s exports, because on average, they are seven times further away.

The second reason is that trade with the "world outside" is not the unalloyed good that many disciples of free trade imagine. After he came to power in 1978, Deng Xiaoping’s pro-market reforms allowed China to make use of its comparative advantage in low-cost manufacturing. Other developing economies followed. This process enriched Britain’s consumers: electronic goods, toys, clothes and steel became much cheaper in real terms. And over time, labour and capital were redeployed to more productive sectors of the British economy, raising incomes further. Together, these two effects made Britain richer on average.

However, those last two words – "on average" – matter. Trade with poorer countries is not without cost. The scars of deindustrialisation are still visible in Britain’s unbalanced economy, with higher unemployment rates and lower productivity continuing to blight the UK’s northern cities. As manufacturing and industrial work dried up, many low-skilled people moved into poorly paid services jobs. Productivity growth in these sectors has been slower than in manufacturing. These trends have contributed to the "hollowing out" of the British labour market, with more low- and high-paid jobs being created than those which provide middling earnings. That does not mean that an "independent" Britain should avoid a trade agreement with China – but it does suggest that agreements with richer countries should be its priority.

After the 2008 crash, Britain’s productivity plunged and then stagnated. It had been catching up with US levels over the preceding decades, but after six years of weak growth, the UK’s output per worker is now a quarter lower than the US. Thus Britain’s trade strategy should make productivity growth its ultimate aim. This points us to the third reason why Britain needs untrammelled trade with the EU: imports, especially from rich countries, are more valuable than exports, because they help to boost productivity. And in the long run, it is productivity growth which determines our economic growth.

The way this works is that imports boost competition in the domestic economy, which raises the incentive for domestic firms to make productivity-enhancing investments and to invent new technology – wringing more output from workers and machinery. These improvements are known as the "dynamic gains from trade". Hence, the constant pressure of competition from more productive overseas companies raises productivity growth.

Yes, a free-floating Britain could unilaterally and fully open its markets to the US, Japan, Australia and the EU in order to take advantage of those dynamic gains. But it might not actually eclipse what we already get from the EU. One of the largest sources of dynamic gains is foreign direct investment (FDI). Britain is the largest recipient of FDI in the EU because it offers a perfect bridgehead for European markets: connected to the free trade zone, but with a labour force that speaks English and low taxes and regulatory costs. Leaving the EU would endanger this investment, because we wouldn't be able to control what kind of tariffs and other restrictions the EU might choose to impose on it. Already Nissan, whose Sunderland factory now produces more cars per year than Italy, has plants elsewhere in the EU, and higher trade costs would only prompt it to expand production inside the single market.

So in our imaginary "year zero" scenario, these rules would give Britain's negotiators a clear order of priorities. First, seek to open markets with more productive, rich countries. Second, seek to open markets with countries that are nearby. Measures to boost exports with distant emerging economies come third.

If Britain votes to leave the EU, it might be possible to negotiate continued market access with a ban on any behind-the-scenes discrimination against British companies in EU member-states. But this would be difficult politically. The EU would demand that Britain sign up to all single market legislation – so Westminster would not be allowed to repeal unwanted EU regulation. And we would have less sovereignty, not more, because we would lose our vote on new EU rules. The UK would also have to continue paying budget contributions and accept unrestricted immigration from the EU.

Since those divorce terms would be hard for the UK to accept, Brexit would be likely to raise trade barriers with the EU. We would be poorer for it.

John Springford is a senior research fellow at the Centre for European Reform