“What goes on in your mind?” sang the Beatles in 1965. It’s a question we’ve been given cause to ask of some leading Brexiteers and the media megaphones of the Leave movement in recent days.

We’ve been told by some of them that there is zero evidence of any kind of hit to the economy as a result of the British vote to leave the European Union. Yet we’ve also been informed that the economic damage since 23 June is a result of malevolent “Remoaners” talking down the economy.

We’ve been assured that the financial markets have responded with perfect calm, even enthusiasm, to the referendum result. Yet we’ve also been lectured that the plunging pound is nothing to worry about but something that will actually benefit us by enhancing the competitiveness of our exports. Strangely, some of these obviously incompatible arguments have been put forward by the same individuals.

But actually the cognitive dissonance goes much deeper than the short-term response to the referendum vote.

Theresa May says she has an 'open mind' over Brexit negotiations

Many leading Brexiteers claim to be ardent Thatcherites. Yet the creation of the modern European single market in goods and services, which we seem to be about to quit, was very much Margaret Thatcher’s project. Her ministers are said to have described the rule-harmonising Single European Act that she signed in 1986 as part of the “Thatcherisation of Europe”.

Most Brexiteers on the right profess their attachment, even devotion, to free markets. Yet their enthusiasm dries up when it comes to the free movement of people, which is necessary to make a transnational single market in services work efficiently.

Manufactured goods can be shipped. But services, which constitute the bulk of our economy and a vital element of our exports, often can’t be delivered remotely. You can’t sell a haircut to Italy via Skype. And it’s rather difficult to offer a university course to a Slovakian student without them actually coming to study here.

“Out – and into the world” blared the cover of The Spectator magazine before the referendum vote, arguing that a Leave vote would unshackle Britain to sign new bilateral trade deals with the rest of the world, presumably involving UK services firms.

Yet as an excellent report last week from the Institute for Fiscal Studies pointed out, major new trade deals that cover services with other countries will inevitably require regulatory harmonisation between us and our trading partners; precisely the kind of harmonisation rules that the Brexiteers detested when they emanated from the European Commission.

Brexit reactions – in pictures Show all 10 1 /10 Brexit reactions – in pictures Brexit reactions – in pictures Supporters of the Stronger In campaign look at their phones after hearing results in the EU referendum at London's Royal Festival Hall AP Brexit reactions – in pictures Leave supporters cheer results at a Leave.eu party after polling stations closed in the Referendum on the European Union in London Reuters Brexit reactions – in pictures Mr Cameron announces his resignation to supporters Getty Brexit reactions – in pictures Donald Tusk proposes that the 27 remaining EU member states ‘start a wider reflection on the future of our union’ Getty Brexit reactions – in pictures Ukip leader Nigel Farage greets his supporters on College Green in Westminster, after Britain voted to leave the European Union PA Brexit reactions – in pictures Supporters of the Stronger In Campaign react as referendum results are announced today Getty Brexit reactions – in pictures Boris Johnson leaves his home today to discover a crowd of waiting journalists and police officers Getty Brexit reactions – in pictures Leave EU supporters celebrate as they watch the British EU Referendum results being televised at Millbank Tower in London Rex Brexit reactions – in pictures Supporters of the Stronger In Campaign react as results of the EU referendum are announced at the Royal Festival Hall Reuters Brexit reactions – in pictures Supporters of the Stronger In campaign react after hearing results in the EU referendum at London's Royal Festival Hall PA

It’s unclear why this legal convergence will be any less noxious to Brexiteers, any less of an infringement on “sovereignty”, when it is involves the US, Australia, China, or whoever else we manage to do these bilateral deals with.

The awful thought occurs that we might be compelled by these sovereignty fetishists to “take control” of our nation’s laws all over again when a new process of regulatory convergence kicks in.

This underlines the central distortion of the Leave case. The regulation and harmonisation directives from Europe were not some kind of sinister plot to create a European superstate, not “foreigners telling us what to do”, as the Brexiteers claimed, but rather a necessary condition for the deepening of the single market in services.

The thing about foreigners telling us what to do is that we also get to tell foreigners what to do; for instance, we can tell them not to erect illegitimate non-tariff barriers to British firms selling in their domestic markets.

The deepening of the single market has enabled our accountants, doctors, architects and bankers and many other professions to sell more services to Europeans than they otherwise would.

It’s true that the single market in services is still very far from complete. But walking away from membership will still undoubtedly hurt these sectors – and that will, in turn, be harmful to the British economy.

What’s the alternative? Some Brexiteers talk about the huge potential of new free trade deals, such as the one signed between Canada and the EU. But such agreements are primarily about scrapping tariffs and are thus of benefit to manufacturers rather than services firms which are hampered by non-tariff barriers.

And other Brexiteers (the only ones who have even attempted any economic modelling) are apparently happy to wipe out the UK’s manufacturers by calling for the unilateral scrapping of all import tariffs.

This would expose the UK to, among other things, a tidal wave of imports of cheap and state-subsidised Chinese steel. Kiss goodbye to Port Talbot and the rest of the UK steel industry if they get their way.

Brexiteers profess to hate needless bureaucracy. Yet, as the IFS report also makes clear, leaving the single market will result in customs checks for our manufacturing exporters since the EU states will suddenly need to identify the “country of origin” of all our goods to make sure that the single market is not being compromised. That’s even if we sign a free trade deal to eliminate tariffs, by the way.

And even the “soft” Brexit of European Economic Area membership, which keeps us inside the single market, will mean customs checks for British exporters. Just ask Norway.

We don’t know much about the shape of the UK’s future trade relations with the EU. But one thing we can be pretty sure of is that there will be officials with clipboards checking containers of British goods arriving in Rotterdam and other mainland European ports. If UK exporting firms don’t like this they should take it up with the anti-red-tape Brexiteers.

But the apogee of Brexiteers’ cognitive confusion surely relates to their reading of European politics. The same people who have portrayed European leaders as a lethal amalgam of ideology, incompetence and malevolence now blithely insist these same politicians will shortly be enveloped by a spirit of generous reason and practical enlightened self-interest when it comes to hammering out a deal with the UK.

The Germans won’t want to hurt their own car industry by driving a hard bargain on trade, we’re airily told. Are these the same Germans who, we were previously warned, had deliberately ruined Greece to teach Athens a lesson?

Are these the same European zealots who are trying to finish the work of Napoleon and Hitler? Did these fiends become pussycats overnight on 23 June?