SIX months ago the chances that Britain would leave the European Union—Brexit—were remote. Today, largely because of Europe’s migration crisis and the interminable euro mess, the polls have narrowed (see article). Some recent surveys even find a majority of Britons wanting to get out .

David Cameron is partly responsible, too. Fresh from his election victory, the prime minister has embarked on a renegotiation to fix what he says is wrong with the EU and is committed to holding an in/out referendum by the end of 2017. But Mr Cameron is in a bind. It is fanciful to believe that the small changes he may secure will convert those who instinctively favour Brexit. And yet he can hardly argue that the EU is just fine as it is—otherwise his renegotiation would be needless.

Mr Cameron is hoping to emulate his Labour predecessor, Harold Wilson, who also renegotiated and then won a referendum on Britain’s membership in 1975. But this time more Tory MPs want to leave than Labour MPs did then. More newspapers are Eurosceptic: in 1975 only the communist Morning Star backed the Outs. The Out campaign is better organised and financed. And the rival In campaign, which was launched on October 12th, is coming to the debate late. If Britain is to avoid Brexit, the time has come to expose the contradictions in the Eurosceptic case for leaving. Fortunately, they are glaring.

Brexit delusions

The Utopia of globally minded Eurosceptics is a British economy set free from burdensome Brussels regulation, retaining access to Europe’s single market, no longer paying into the EU budget, trading freely with the rest of the world and setting its own limits on immigration. Yet as our special report this week sets out in detail, every part of this ideal is either questionable or misleading.

Take regulation. The Paris-based OECD club of mostly rich countries says that Britain has the least-regulated labour market and second-least-regulated product market in Europe. The most damaging measures, such as planning restrictions and the new living wage, are home-grown. Post-Brexit Britain would almost certainly choose not to scrap much red tape, since the call for workplace, financial and environmental regulation is often domestic and would remain as strong as ever.

Moreover, if Britain wanted full access to the European single market, it would have to observe almost all the EU’s rules. That is the case in Norway and Switzerland, non-members that both also pay into the EU budget (in Norway’s case, roughly 90% of Britain’s net contribution per head). Eurosceptics who dream of reclaiming lost sovereignty need to explain how they advance their aims by advocating an alternative that would require Britain to apply rules it has no say in making—and to pay for the privilege.

If, instead, Britain wishes to escape the EU’s rules, it will lose full access to the single market. The argument that, because Britain imports more from the EU than the other way round, it is in a strong bargaining position is unconvincing: the EU takes almost half of British exports, whereas Britain takes less than 10% of the EU’s. A free-trade deal in goods might be negotiable, but it would not cover services (including financial services), which make up a rising share of British exports. And one thing is sure: if Britain establishes a precedent by leaving, the rest of the EU will not rush to reward it.

Next is the assertion that a post-Brexit Britain could trade more with dynamic economies beyond Europe. Leave aside the fact that German exports to China are three times as big as Britain’s. The broader objection is that a Britain in search of free-trade deals with these giants would lose the negotiating clout of belonging to the world’s biggest single market. A prime example is the Transatlantic Trade and Investment Partnership being negotiated by America and the EU (see article). A post-Brexit Britain would be excluded from TTIP.

Explore our interactive guide to Europe's troubled economies Then there is migration, today’s most emotive issue. Switzerland’s and Norway’s experience suggests that if post-Brexit Britain wants full access to the European single market, it will have to accept the free movement of people from the EU. Leaving the EU would not stop refugees from crowding into Calais, but they would be harder to manage, because co-operating with France would become more problematic. Liberal Eurosceptics favour more immigration and a more global Britain. But that is a pipe-dream. If Britain leaves the EU it will be precisely because a lot of voters mistrust foreigners and globalisation. After Brexit, they will expect a more inward-looking Britain that imposes tougher immigration controls. The final contradiction is over British influence. Eurosceptics say that Britain must leave because it counts for nothing in Brussels and is constantly outvoted on policy. Yet at the same time they argue that, with the world’s fifth- or sixth-biggest economy, a post-Brexit Britain would punch well above its weight internationally and be able to strike favourable commercial deals around the world, including with the EU it had just voted to leave.

Influence peddling

In fact Britain has influenced the EU for the better. The European project it joined in 1973 had obvious flaws: ludicrously expensive farm and fisheries policies, a budget designed to cost Britain more than any other country, no single market and only nine members. Thanks partly to British political clout, the EU now has less wasteful agricultural and fisheries policies, a budget to which Britain is a middling net contributor, a liberal single market, a commitment to freer trade and 28 members. Like any club, it needs reform. But the worst way to effect change is to loiter by the exit.

Mr Cameron is waking up, belatedly, to the threat of an Out vote. Were it to happen, he would surely have to resign, to be replaced by a more Eurosceptic Tory leader. In Scotland the first minister has again made clear that if Britain leaves the EU she will seek a vote for independence (she would probably win). The break-up of the United Kingdom and the end of Mr Cameron’s premiership: Brexit would produce large political fallout. Mr Cameron must fight harder to prevent it.