The Labour party now supports Britain remaining in a customs union after Brexit. That is also the view of at least 10 Conservative MPs, such as Anna Soubry and Nicky Morgan, who have put an amendment to this effect in the Commons. Theresa May’s government therefore faces a real danger of being defeated on this issue by a cross-party coalition. It is easy to see why continued membership of a customs union appears so attractive. It would seem to allow frictionless trade without committing Britain to free movement, budget payments to the European Union, or supervision by the European court of justice (ECJ), and no hard border in Northern Ireland.

The only major country outside the EU with which it has a customs arrangement is Turkey. This was proposed when it was believed Turkey might eventually join the EU. It is unclear whether this would be available for a country that had decided to leave Europe. But even if it were, the deal is highly disadvantageous to Turkey, and would be even more so to Britain.

Q&A What is a customs union? Show Hide A customs union means that countries agree to apply no or very low tariffs to goods sold between them, and to collectively apply the same tariffs to imported goods from the rest of the world. International trade deals are then negotiated by the bloc as a whole. For the EU, this means deals are negotiated by by Brussels, although individual member state governments agree the mandate and approve the final deal. The EU has trade deals covering 69 countries, including Canada and South Korea, which the UK has been attempting to roll over into post-Brexit bilateral agreements. Proponents of an independent UK trade policy outside the EU customs union say Britain must forge its own deals if it is to take advantage of the world’s fastest-growing economies. However they have never explained why Germany manages to export more than three times the value in goods to China than Britain does, while also being in the EU customs union. Jennifer Rankin

Play Video 3:35 Jeremy Corbyn: UK should remain in a customs union with EU – video

Intrinsic to the idea of a customs union is that goods cannot enter into it without paying the agreed common external tariff. Therefore only the European commission, and not individual countries, can negotiate trade deals with third countries. So Britain would not be able to negotiate independent trade deals with third countries that involved the lowering of tariffs. That would remove one of the principal advantages of Brexit: the opportunity to secure lower prices for consumers by importing goods tariff-free from outside the EU.

In addition, when the EU negotiates a trade deal with third countries, the deal would open up British markets to these countries; but it would not open up their markets to Britain, since Britain would not be a member of the EU. The Turks were worried that, should the US-EU negotiations over the proposed Transatlantic Trade and Investment Partnership prove successful, American goods would be able to enter Turkey tariff-free, but Turkish goods would still face US tariff barriers in the US.

A customs-union Britain would therefore have to conclude separate trade agreements with third countries so as to secure the benefits of the EU deal. But there would be little incentive for third countries to conclude such agreements, since their goods would already be able freely to enter Britain. We would be, as Barack Obama said in another context, at the back of the queue.

There cannot be different sets of standards or regulations between different members of a customs union

While it is true that membership of a customs union outside the EU would free Britain from the jurisdiction of the ECJ, there would have to be some sort of body capable of arbitrating disputes between Britain and the EU. That body might be the court of the European Free Trade Association (Efta), or it might be a nonjudicial body. But whichever it was, it would in practice have to broadly follow ECJ rulings, as the Efta court does. There cannot be different sets of standards or regulations between different members of a customs union, for that would allow a country to subvert the common tariff.

So Britain would have to align itself not only with EU trade policy but also with the laws of the EU in certain areas: not only as they are now but also as they may be altered in years to come – except without a vote to help decide on them. Britain would be subject to regulation without representation, the very relationship that led the North American colonies to break away from Britain over 200 years ago.

But perhaps the greatest illusion shared by supporters of a customs union is that it would promote a frictionless border. Anyone who has seen the queue of Turkish lorries at the Bulgarian border, sometimes extending 10 miles – a two-mile queue is considered a good day – will realise that this is not the case.

The 60,000 lorries sent from Turkey to the EU every year are required to carry a host of documents, including an export declaration, invoices for the products they are carrying, insurance certificates and a transport permit for each EU nation they intend to drive through. These permits, which are set by agreement with individual countries, can be made subject to quotas.

The EU has so far agreed to frictionless trade and open-access road transport only for countries that accept free movement – members of the European Economic Area (Norway, Iceland and Liechtenstein) and Switzerland, which has bilateral agreements.

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The truth is that there is no such thing as a “soft” Brexit without making Britain in effect a client state of the EU. From that point of view, May was absolutely right to have declared that Brexit means Brexit.

The real choice facing Britain is stark: between a “hard” Brexit, and remaining in the European Union.

A hard Brexit – in which the UK retains complete freedom to diverge as much as it likes from the EU – would work only if we were to follow the example of New Zealand and seek to become a global hub by adopting a free-market policy of radical deregulation, drastic cuts in personal and company taxation, the ditching of agricultural subsidies, and the unilateral removal of tariffs. It is, however, difficult to believe the British public would be prepared for so drastic a dose of renewed Thatcherism.

But the choice should be made by the people and not by parliament. And in due course not only the remainers but perhaps also the government – deeply split, like the country, on the issue – will realise that it is in their interests to call a second referendum.

• Vernon Bogdanor is professor of government at King’s College London