Sketch: When Miliband met Mitt

A Labour leader striking up an unexpectedly warm relationship with a Republican president: haven't we seen all this before?

It's a sunny, sweaty morning in Westminster. The place is deserted now MPs and peers have flown off for their summer holidays. Well – almost deserted. In the leader of the opposition's office, an American presidential candidate is shaking hands and smiling.

Your correspondent wasn't in the room when they entered. This delay had nothing to do with the Olympics: Ed Miliband's office is nigh on impossible to find at the best of times. And, as it happens, I wasn't late. But something extraordinary was happening. This meeting was taking place on time.

Two burly looking men in sharp black suits, out of which emerged earpieces, muttered to themselves. Staffers peered into the room. A line of journalists, some familiar and some not, mixed in with Labour officials looked on at the unseen pair. Shadow foreign secretary Douglas Alexander was among them, looking sage and considered.

And there they were, Romney smiling his perfect smile as Miliband continues his Most Statesmanlike Week Ever. Ed was talking about the Olympics and is looking forward to their talks. Then Romney took over.

"Mr Leader," he declared to Miliband. Is this an Americanism, or had he mistaken Red Ed for Kim Jong-un? North Korea-themed gaffes seem to be unexpectedly 'in' this week, after the flag mix-up at the football last night. When that's raised Romney is very diplomatic. "Of course there will be errors from time to time," he said, with the relaxed insouciance of a man who couldn't care less. "But those are all overshadowed by the extraordinary demonstration of courage and character shown by the athletes".

He seemed fixated on the "heroics" of those taking part in the Games, but Romney couldn't help lauding the American and British "mili-tairy" in Afghanistan, either.

Mitt'n'Ed did that hopelessly gormless thing whether their arms just hang down by their sides – it's better than fidgeting, they've been taught. Eventually Miliband gave up and placed the tips of his fingers together. This is well-known as being in the top five power gestures of all time, and so very appropriate for a young party leader trying to make his mark on the international stage. No-one in the room seemed to think it makes him look like he'd had a terrible accident with superglue.

After the first question, which focused solely on the Olympics and on Romney's view of them, Miliband butted in. "There is a special relationship between Britain and the United States," he blurted out, apropos of nothing. Romney didn't flicker an eyebrow. So Miliband pressed on. "Expressed in our shared history," he added, giving Romney a quick prompting, pointed glance. The Republican gave the slightest of nods, inclining his head gravely.

It was over almost before it began. At the end of an awkward two-part question Romney's American handlers – there are a small army of them – were the picture of decisiveness. "That's it folks," or "thank you, that's it," or – well, you get the picture. But Romney was happy to pause to answer the tricky question about Britain's economic policies. "While I am on foreign soil I am very careful to be critical of my own government's policies," he said, smiling.

"It would be even more remiss of me if I were to be critical of any other government's policies." And there it is: just a hint of genuine charm, a practised ease, a well-oiled informality to bring the session to a close. Romney will have had Obama's warning that "America's political differences end at the water's edge" ringing in his head when he said it.