The plot by the European Union to subvert British democracy has to be one of the world's worst conspiracies. Every prime minister since Edward Heath has apparently colluded in this nefarious project, and yet, stubbornly, the UK still governs itself.

You get a much higher calibre of conspirator in Washington. They assassinate presidents and fake moon landings. Brussels can't straighten a banana without the bloodhounds of the conservative press unearthing the story.

But things are looking up for the plotters. A second Irish referendum has approved the Lisbon treaty, removing one of the last obstacles to its taking effect. This document, remember, is a European constitution in disguise, smuggled through Britain's parliament under the noses of somnolent MPs. It means that Albion's ancient powers can be whisked away at last to a dark Belgian corridor.

There is another interpretation: that there is no conspiracy; that the EU is an alliance of sovereign nations in which British prime ministers have collaborated because it serves the country's interests; that the Lisbon Treaty is just one in a parade of flawed but worthwhile compromises required to make a multinational alliance work. Dull, but true.

Full-bodied fear of the EU exercises only a small minority in Britain. But the underlying theme – that "Europe" and Britain are adversaries in a zero-sum game of power and influence – is deeply embedded in mainstream discourse. It is an idea that badly misrepresents where our national interests lie. Sadly, it is also about to become a guiding principle in our foreign policy, and at a time when the case for sensible pan-European accord has hardly been stronger.

There are various factors explaining why Ireland voted "yes" in Friday's poll, despite having declared the opposite 16 months earlier. There were symbolic concessions in the terms of the treaty and a better organised pro-Lisbon campaign. But a crucial intervention was made by the financial crisis, which threatened to hollow out the debt-laden Irish economy as it did Iceland's. The difference is that Ireland, as a member of the eurozone, was propped up by the European Central Bank.

The Lisbon Treaty actually says nothing about financial assistance. That is beside the point. The real threat of national bankruptcy put the theoretical threat of diminished national autonomy in its place. Unregulated global finance, it turned out, was more hostile to sovereignty than the EU.

Ireland's calculation describes, in essence, the whole point of the European project: negotiated political integration is a source of security, stability and strength.

The financial crisis has not exactly wrapped Europe in a cosy blanket of cross-border solidarity. It triggered protectionist impulses in bigger member states with the capacity to protect flagship industries, German and French car makers in particular.

But the crisis has focused continental minds on the relative punching weight of European nations in a globalised world. Individually, they are bantam at best. Witness Gordon Brown in New York last week, self-styled saviour of global finance, humbly supplicating Barack Obama's aides for an audience with the chief.

For most of the 20th century, Europe was the world's front line: two savage hot wars, and a long, brutish cold one. Our continent threw the parties and everyone came.

The 21st century will be different. China and India already lay claim to superpower status. Russia imperiously waves its nuclear arsenal and natural gas reserves as a VIP pass to international summits. Brazil has economic and diplomatic aspirations equal to its geographical expanse.

That doesn't mean Europe is in decline, or that individual states must subordinate their interests. It simply means that the rivalries of last century need to be held in perspective against the advantages of collaboration on a range of global issues: trade, security of energy supply, cross-border crime, climate change, migration, financial stability.

Whether the EU can forge a common position on those things is one of the biggest foreign policy challenges of our times. It would be reassuring if Britain was ready to play its part. It isn't.

That is partly a result of political accident. In 2005, to secure the Conservative party leadership, David Cameron made promises to anti-EU Tory backbenchers. It must have seemed like a good deal: important for the party faithful, unnoticed by most British voters. But the effect was to grant snarling Europhobia immunity from modernisation.

Now Cameron is locked into intransigence. His policy is to hold a referendum, and advocate a "no" vote, if Lisbon is not in effect when the Tories form a government. If the treaty is active, he and William Hague say they will "not let matters rest". That isn't so much a policy as a beach towel on the sun lounger of a policy; absence signalling stubborn intent.

In reality, Cameron will have two options. He can call a referendum anyway, which would sabotage the ratified treaty and enrage other EU governments. Or, he can acquiesce to Lisbon and confect some symbolic mechanism to "repatriate" power. But any compromise that does not involve a plebiscite will still be viewed by the right as treason. The referendum is of totemic significance to hardline sceptics. They see the EU as a device that transfers power from the people to "Brussels" and a national vote as the only way to put a spanner in those works.

But the underlying assumption that "Brussels" perpetrates indignities against Britain is false. Real power in the EU is exercised by national governments, mandated by popular election. Under EU treaties, including Lisbon, the vast majority of decisions made in "Europe" that have an impact on Britain, are made with British sovereign consent.

The only sneaky part of the process is that national governments indulge the illusion that power is located elsewhere – in the hands of "faceless bureaucrats" – to avoid scrutiny of their decisions.

Labour and Tory prime ministers have been equally guilty of that subterfuge, heading off to European summits with a pretend list of national treasures to be protected; returning with a pretend list of trophy concessions that have been won.

But David Cameron will not be able to play that game. The point of Lisbon is to put an end to tedious tinkering at the EU decision-making process, so Europe can start making decisions. Other powerful leaders, Germany's Angela Merkel and France's Nicolas Sarkozy, will have no patience for a British counterpart who turns up spoiling for a fight.

There are urgent areas of policy where the EU has to negotiate continental bargains, from curbing carbon emissions to regulating banks. A government that scorns the principle behind the bargaining process will lose out. In opposition, fear of a European stitch-up at Britain's expense is paranoid; in government it will be self-fulfilling prophecy.

Scepticism is a healthy position to take towards grand political projects, especially when, like the EU, they are infused with the vanity of statesmen. But the kind of parochial phobia that is normal in Britain's discussion of the EU, and that informs the mainstream of Conservative policy, is not scepticism. It belongs in a whole different category, alongside climate change denial and the 9/11-was-a-CIA-plot "truth" movement. It is lazy and wrong. Now is hardly the time to put it at the heart of Britain's foreign policy.