“We must do it. It’s the price we pay to sit at the top table.” Those were the words with which Winston Churchill decided to continue Britain’s efforts to develop its own nuclear bomb in 1954.

Although those words themselves are absent from Tony Blair’s communications with George W. Bush or British ministers in the run-up to the Iraq war, their spirit is on every page. In a way, that the Chilcot inquiry is damning of the Blair government’s approach in the build-up to war shouldn’t be a surprise; it is no more damning than any of the serious studies of the period, whether in Andrew Rawnsley’s End of the Party, or the historians Anthony Seldon and Peter Hennessy’s accounts of the build-up to war.

We already know that post-conflict planning was threadbare to non-existent, that Blair had already privately pledged that he would back Bush, and that the case for war was inflated. What is remarkable about Chilcot’s inquiry is that it gives what we already knew the official imprimatur.

But there’s a danger, post-Chilcot, that we see the disaster of Iraq as a unique one in British history, when in fact it is simply the most bloody manifestation of the delusion of outsized British influence, over the world in general and the United States in particular, a delusion that, for the most part, requires the expenditure of considerable monies from the Treasury in exchange for very little in terms of real influence.

It was Harold Macmillan who envisaged the British role as the “Greeks in this American empire”. “Like the Greeks of old,” Macmillan argued, “[Britain]must teach them how to make it go.” Macmillan was a classical scholar – but he had overlooked that the most important feature of the Greek slave in the Roman court was not influence, but bondage. It was only towards the end of his premiership that he began to realise the limits of British influence – and began, belatedly, to push for Britain to join the Common Market (now the European Union).

Although for most of British postwar history it has been the right’s imperial delusions that have guided British foreign policy, the left hasn’t been immune either. As AJP Taylor, the historian and unilateralist, observed of CND’s failed efforts in the 1950s and 1960s:

“We made one made mistake which ultimately doomed CND to futility. We thought that Great Britain was still a great power whose example would affect the rest of the world. Ironically, we were the last Imperialists. No one cared in the slightest whether Great Britain had the bomb or did not have the bomb. The Russians were not frightened because we had it. The rest of the world would not be impressed if we gave it up.”

We see this in some of the commentary that has already emerged post-Chilcot, which presents the British as key actors in the tragedy. But while the United Kingdom has equal complicity with the United States, it did not have joint authority. As Chilcot writes, the Americans had decided to embark on the war in Iraq in 2001, and as the histories already written show, Bush had told Blair than the White House could push on alone if the political backdrop made British assistance impossible.

We also have the counterfactual of Vietnam, when another Labour Prime Minister, Harold Wilson, opted to stay out of an American-backed horror.

That matters because while the political passion for large scale intervention has been at least temporarily extinguished by the failure of Iraq, British exceptionalism – the other pillar of British involvement in Iraq – is alive and well. We saw that in the campaign to leave the European Union, and the accompanying inflated promises for the deal that could be struck by Britain after a Brexit vote. British policymakers risk taking only one lesson from Iraq - don't start long wars - when they should take two: that the myth that the British voice can influence global events or the United States alone is just that: a myth.