The third post-1945 invasion was just as momentous, yet official and media silence about it is usually deafening. Since 1947, there have been US military bases in the UK: something that would have been unthinkable before 1939.

Schoolchildren in the United States are still taught that London's decision to keep 10,000 troops in the colonies after 1763 was one of the precipitants of the American revolution. Yet, according to the available statistics, over 10,500 US military personnel were stationed in the UK as late as 2005, a higher total than in any other European state, barring Germany and Italy, both defeated in the second world war. In all, well over 1.3 million US personnel have been stationed here since 1950, without - so far as I know - any consultation of the electorate.

It is not the exact number of these troops, however, but what they represent that is significant - namely London's postwar position of considerable clientage to Washington in terms of foreign policy and much else.

To refer to these subjects is to invite accusations of anti-Americanism. But I am not anti-American. I have worked in the US for 20 years. My point is not American power, but rather the double standard that characterises so much British political discourse. Sections of the media and members of both major parties have been all too eager to bang the autonomy drum when it comes to Europe. But there is a marked unwillingness to analyse the challenges to British independence from US influence; and those touching on the subject are swiftly denounced.

The usual rationalisation for this double standard is that the EU threatens Britain's internal way of life, while its relationship with the US does not. This is palpably absurd. Even leaving aside its military bases, America's influence on the domestic ordering of British life has been enormous, though sometimes unrecognised. The central place of deposit for Britain's historic archives at Kew, for instance, used to be called the Public Record Office, but is now re-named the National Archives. Why? Presumably because this is what the US styles its central place of archival deposit in Washington.

American influence has had far more portentous consequences. As Timothy Garton Ash recently remarked on these pages, people in Britain are subject to some of the most extensive official surveillance in the world. One excuse for this is the threat from terrorism. Would this threat be as great without our participation in the Iraq war? And would Britain have participated in that war had it not been so accustomed to following Washington's foreign-policy lead?

Why are large sections of Britain's political class seemingly at once so enamoured of America, yet so nervous of Brussels? The argument that this reflects traditional ties between English-speaking peoples won't do. As historians like Kathleen Burk and Paul Kennedy have documented, before 1914 (and even after in some cases) members of Britain's political elite were more likely to be pro-German than steadfastly pro-American. Even in the 1920s, Winston Churchill was adamant that "we do not wish to put ourselves in the power of the United States". So when David Miliband feels obliged to argue that Europe can aspire only to be a regional power, not a great power (which might conflict with US interests), this reflects less a long tradition of transatlantic amity than a degree of British diffidence in the face of Washington that has arisen since 1945.

The obvious reason for this has been the extent both of America's postwar power and Britain's postwar decline. Postcolonial critics are, I suspect, wrong when they argue that the mass of British people still mourn the loss of empire. But Britain's politicians - and its Foreign Office - have found it hard to adjust to the loss, not so much of onetime colonies, as of the global clout the colonies once afforded. "Poor loves", the novelist John Le Carré has one of his characters declare from Oxford (alma mater of both Tony Blair and David Cameron): "Trained to empire, trained to rule the waves. All gone. All taken away. Bye-bye world."

Shadowing Washington allows official Britons who still hunger for the big stage some continued admission, even if it is only as supporting players. And there is a further consideration that underlines how closely foreign policy has been bound up with postwar British anxieties. Conservative and Labour governments have arguably championed British rights in Brussels so ostentatiously in order to deflect public attention away from their deference to Washington. But British official suspicion of Europe also stems from the challenge it undoubtedly represents to the union. Scottish and Welsh nationalists, like the Irish Republic before them, favour much closer involvement in the EU precisely because they believe this will lessen their countries' dependence on Westminster.

Indeed one of the problems with current debates about "Britishness" is that they focus too exclusively on domestic identities and values. Addressing the question of what Britain is, and of how far it can plausibly function as an independent and united polity, requires a far more informed and even-handed public discussion than exists at present about our relations with both America and the rest of Europe.

Such a discussion might be uncomfortable for more than just the politicians. Since 1945, Britain - like much of Europe - has been tacitly involved in a massive bargain. The US has bankrolled large sectors of our defences, and thus allowed our governments to plough money into various social programmes instead. The EU - and Miliband was right on this - is itself not remotely close to possessing the kind of firepower that would underpin the vast ambitions of its more ardent supporters.

To this degree, dependence on the US is inescapable, and is likely to be so for some time. There has been a reluctance to spell this out, and even more of a reluctance to address what might happen if US power recedes in the future to the degree that some American commentators are now predicting. Would English, Welsh, Scottish and Northern Irish taxpayers be willing to pay more for defence if this meant being less entangled with US priorities and pressures? As is true of our foreign relations generally, public debate on this issue has barely begun.

· Linda Colley is professor of history at Princeton University and the author of Captives: Britain, Empire and the World, 1600-1850

lcolley@princeton.edu