For a poignant vignette of Britain's fabled "special relationship" with the United States, you should know that back in the day, visitors to Tony and Cherie Blair's small private flat above Downing Street would note that they had prominently displayed no fewer than four pictures of themselves with the Clintons. How many do you reckon Bill and Hillary had of themselves with the Blairs? I'd guess the full nought, though perhaps the help would have been charged with sticking a small one up in one of the meeting rooms each time the couple paid a fawning visit in their capacity as Dearest Allies.

Just memories now, alas, but owing to Barack Obama's perceived snubbing of Gordon Brown at one of the 37 summits taking place this week, there has been much talk of "another blow" to the special relationship, as though it were possible to land one on something that doesn't exist. Without wishing to let daylight in on the magic only certain British politicians can see, the special relationship is cobblers. It is the kind of imagined relationship that a stalker has with the distant target of their affections, whose oblivious "snubs" are taken weirdly, terribly personally.

I need hardly tell you which role is taken by Blighty. We're Partridgean mentalists, plastering our house with photos of our crush, and have been ever since Churchill coined the "special relationship" phrase, knowing even as he did so that he was being done over by the Americans on lend-lease. Three years ago a senior State Department adviser stated that the special relationship was a "myth". "It has been, from the very beginning, very one-sided," Kendall Myers explained starkly. "There never really has been a special relationship – or at least not one we've noticed."

Quelle bitch! But he's right, of course. There have been special interpersonal relationships, like Callaghan and Ford, and Reagan and Thatcher, although the latter became irrationally crestfallen when Ronnie forgot to mention to her that he was invading Grenada. But for all these pashes, the upshot has been a catalogue of give and take. We give; they take. And who can blame them?

One of the many geniuses of Armando Iannucci's movie In the Loop was the way it showed how that lopsided, anxiety-riven puppy love percolates all the way down the chain of power, with even bag carriers fretting about how to secure face time with their imagined opposite number. From PMs to PAs, we're always the rubes in Washington, giddily grateful to be near the seat of real power, scarcely one up from the real-life tourists who gawp their way round the West Wing. The syndrome is part of our national political makeup, and the minute anyone accedes to power they crave the pat on the head they probably once swore they didn't give a fig for. He might be standoffish now, but allow me to go out on a limb and wager that David Cameron – who already has plans to reconfigure Downing Street in the mould of the White House West Wing – will do the same. The more protectionist Obama is forced to get, the more desperate to be noticed Cameron will become.

And so it was this week in New York, with reports claiming that Brown's request for bilateral talks had been snubbed by Obama five times. Even the suggestion that the froideur was due to the release of the Lockerbie bomber reinforces the poignancy of the joke, with America's studied refusal to distinguish between Brown's government and the Scottish one run by his old adversary redolent of that familiar inquiry of uninterested Americans to touring Scots: "Scotland? Is that a town?"

Eventually, after some heavily publicised angst, Brown got his "walk and talk", as he and the president took a shortcut out of a dinner through a kitchen. Don't you love the idea that they finally hooked up in the kitchen? It's the anti-cool to the uber-cool of that famous shot in Scorsese's Goodfellas, where the Steadicam follows Henry and Karen into a nightclub via the kitchen entrance.

The New York jockeying, fellow unsophisticates, is what passes for highfalutin diplomacy. And yet, to those of us unable to take such things seriously, it far more closely resembles high school movies like Clueless, or possibly Mean Girls, with Brown in the Lindsay Lohan role. And it isn't the most enormous surprise to find Obama not prioritising Brown, what with the class yearbook having voted him "most likely to … not win the next election".

Still, the PM's got the whole nuclear armageddon thing to take his mind off it for now. But one can't help feeling that with his number looking fairly up, Brown should start acting in the manner of those divas whose best days are long behind them, but who still insist on playing the big I-Am. Whenever the next big summit is (it'll be around in a fortnight at the current rate), British diplomatic aides should fax the prime minister's demands in advance. "Mr Brown's summit rider insists on 37 Diptyque candles (Narcisse), M&Ms with all the brown ones removed, and a public guffaw with the leader of the free world. Otherwise he doesn't come out of his dressing room."

How could it play out any worse?