STANDING eight metres tall, the inflatable Trojan horse outside the European Commission office a couple of years ago was difficult to miss. It was erected by campaigners bearing 3m signatures from Europeans who wanted to scupper the Transatlantic Trade and Investment Partnership (TTIP), a sprawling free-trade deal between the European Union and America. For Brexiteers, such a scene seems ideal to help explain why Britain has to strike out on its own; outside the EU, Britain would no longer be held back by continental trade luddites. Except this anti-TTIP protest took place outside the Commission’s London office. A full 500,000 signatories were British.

Britain’s attitude to free trade is more complex than it seems. In a meeting of the Brexit “war cabinet” taking place as The Economist went to press, ministers were due to thrash out a proposed customs relationship with the EU. At stake is Britain’s ability to strike free-trade deals across the globe. But amid the cabinet in-fighting, what voters think is often overlooked.

At first glance Brits love free trade, or at least say they do. Given the choice, nearly half of voters would opt for the ability to do free-trade deals globally—even if it meant customs controls between Britain and the EU, according to YouGov. Jacob Rees-Mogg, the leader of the Conservatives’ hard-Brexit caucus, can be confident of the support of party members: 70% of them want out of the customs union, according to research from Queen Mary University of London.

But this zealotry is not shared by typical Leave voters. They tend not to like free trade: 50% of them think that Britain should limit imports to protect the British economy, according to data from NatCen Social Research, which gauges public opinion. Barely a fifth believe otherwise. “Better trade opportunities with the wider world” was chosen by only 9% of Leave voters as the main reason for voting for Brexit, far behind legal independence and cutting immigration, according to ICM, a pollster. The buccaneering Brexit put forward by Liam Fox, the international-trade secretary, is opposed—or ignored—by those who supposedly voted for it. In practice, Britons are among Europe’s keenest wreckers of free-trade deals. They were at the forefront of scuppering the planned trade deal with America. More people signed an anti-TTIP campaign in supposedly free-trade-loving Britain than in traditionally protectionist France.

For trade-deal boosters, this makes new and awkward political alliances necessary. Liberal Brexiteers must win over those who voted Remain, who tend to be more open when it comes to trade. Only a quarter of Remain voters support a protectionist approach, with 41% opposed, according to NatCen. But within the Department for International Trade (DIT) officials worry that Brexit and trade are mashed together in minds of Remain voters, turning potential allies into sceptics. “When you say ‘trade’ they hear ‘Brexit’,” says one.

In Westminster, Labour are well-armed to cause trouble. During the EU referendum Jeremy Corbyn, the Labour leader, promised to veto TTIP if elected. Nor was John McDonnell, the shadow chancellor, a fan. He said TTIP was aimed at “reinforcing...corporate global kleptocracy”. Rebellious Conservative MPs have backed Labour-led amendments on trade policy. Outside Westminster, campaigners know how to raise mischief. In Britain, linking TTIP and the idea of American firms eventually gaining access to the NHS was enough to infuriate Middle Englanders, say campaigners. And that was before Donald Trump arrived in the White House.

It was not pure anti-Americanism that drove protests. A deal with Canada—the Comprehensive Economic and Trade Agreement—attracted similar howls, due to the inclusion of measures that let companies sue governments. Campaigners managed to fill town halls even when discussing such trade arcana, says Mark Dearn from War on Want, a charity. The result was stark: Britain delivered a third of the 150,000 responses to a European Commission consultation on these investor-state dispute-settlement clauses—more than any other EU country.

The worry for officials in the DIT is that negotiations this time round will be more visible, risking bigger public protests. In the EU, negotiations took place in Washington, Ottawa and Brussels, faraway lands of which British voters knew little and cared less. British trade deals will be hammered out in Whitehall. “It’s Liam Fox, not some faceless bureaucrat,” says a campaigner.

To his credit Mr Fox is aware of the potential backlash. He wants to avoid a repeat of TTIP, “where a huge amount of work is done only to find the public won’t accept it.” Plus, Mr Fox benefits from an ideological tailwind: overall Brits are increasingly liberal on trade. Although a plurality (36%) still demand a protectionist approach, this number is down from over half since 2003, according to NatCen’s research. Amending unpopular parts of trade deals and guaranteeing stronger protection for the NHS, for instance, would allay concerns.

But there will be other flashpoints. A row last summer over the prospect of importing chicken doused in chlorine from America was an aperitif. After 45 years without an independent British trade policy, political price discovery must be done. British farmers have not had to flex their political muscles domestically for decades, instead relying on their more militant continental peers. But that may change if groups like the National Farmers’ Union feel that farmers’ interests are being sacrificed in favour of industries that are more valuable to the exchequer, such as banking. When it comes to trade, the government is yet to understand fully what voters and business will bear. It must look beyond its internal fight.