The basis of Cameron and Obama's relationship is pragmatism, though it remains as lopsided as ever

President Barack Obama calls David Cameron “bro”, just as President George W Bush addressed Tony as “yo Blair”.

We should not, though, assume that the transatlantic relationship is quite as buddy-buddy as it was in the Blair era. It is looser, more pragmatic and businesslike now. Good.

Of course, even at the height of Anglo-American co-operation, when our fighting forces were in the field together in Afghanistan and Iraq, it was a somewhat lopsided affair, as it was always bound to be. America is a superpower and Britain a medium-sized European one. The UK punched above its weight, thanks not least to the skill and professionalism of our servicemen and women. Sentiment was there, and is there still, in many quarters in Washington. Yet most Americans have never heard of this supposed “special relationship” with the UK. Recent administrations have regarded, variously, Mexico, Canada, China, Japan, Israel, Egypt and Saudi Arabia as “special”. Generally, there has a been a tilt towards the Pacific. The British “special relationship” was always, from an American point of view, an optional extra. If it didn’t work, it could be adjusted, as when they withdrew co-operation over nuclear secrets after a series of spy scandals in the 1950s, and let the British be hung out to dry over Suez in 1956.

Things were not so very different half a century on. In the run-up to the 2003 Iraq war, it was made clear by hawks such as then Vice-President Dick Cheney that the US was going to invade even if the British did not join, and whether or not we managed to persuade our EU partners the French to support a proper UN resolution (which we failed to, of course). For Tony Blair, it was simply a matter of loyalty; he asked whether Britain should be on the side of the most powerful nation on earth, or against it – for him a rhetorical question. The decision for war in Iraq was probably made long before he consulted the Cabinet, still less Parliament, though we are still awaiting the report of the Chilcot Inquiry – scandalously delayed – to tell us more about that.

The result of the Blair-Bush “special relationship” was thus an illegal war, millions of innocent people dead and a toxic legacy that we know all too well today – a resurgent Taliban and the barbarities of Isis.

So who wants a special relationship like the Bush-Blair one? Not Mr Obama, and not Mr Cameron, who always knew he would be unlikely to be able to replicate the closeness of Blair-Bush or Blair-Clinton, let alone Thatcher-Reagan, Churchill-Roosevelt or Macmillan-Kennedy. Sometimes the chemistry is there even when the politics are divergent; sometimes a very similar political outlook can count for nothing, as with Lyndon Johnson’s relationship with Harold Wilson. Both were social democratic reformers, but Wilson refused to send even a token battalion of kilted Scots Guards to get sniped at by the Viet Cong.

And so we now have the American and British premiers discussing important but more pragmatic issues, such as more peaceful ways of defeating terror than invading nations – countering cyber attacks and improving intelligence. The UK is a much diminished military power, even compared with a decade ago. We can continue to punch above our weight, but we have neither the economic nor the military strength to be anything other than a minor partner, special or not. As Mr Obama might advise us: get used to it, bro.