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We are outside the Nasdaq building in Times Square, New York, waiting for David Cameron to emerge. The large electronic advert on the side of building proudly welcomes him to the Big Apple.

Outside a large crowd is gathering but few appear to know why. People are attracted by the security and the cameras. He emerges for a photo call later with some American suits who exude extreme wealth. The motorcade moves on.

New Yorkers who have been forced to wait until the road is cleared angrily push past the security. The mass of humanity sweeps past and the waters close over, leaving no trace of Mr Cameron's brief visit. New York is hard to please.

The prime minister's ostentatious austerity drive continues.

Not content with his commercial flight over the Atlantic, Mr Cameron has chosen to take the train from Washington to New York. And of course, like all acts of thrift, it was much more fun.

Less security, better views, and the chance to pass through Baltimore. "The Wire!" the prime minister exclaimed excitedly. "This is where The Wire is set."

Now that's a rare thing. A prime minister who actually watches something other than the news on television.

One of those odd moments that you experience on these trips. I am standing on top of a building in front of Capitol Hill, sweating gently in the humid Washington air, reciting nursery rhymes with the the prime minister.

I am about to interview Mr Cameron and it turns that we share the same rhyme for those occasions when sound engineers ask for a few words so they can check their volume levels. One, two, three, four five, once I caught a fish alive... five, six, seven, eight, nine, ten, then I let it go again. We laugh.

A brief echo of family life amid a sea of sweat, security and high politics in the heart of Washington DC.

After a day at the White House, a few reflections:

1. I haven't seen a prime minister and a president get on so well since Tony Blair and Bill Clinton. First names only, same coloured ties, lots of gags about the kids. Makes George Bush's line about sharing the same toothpaste as Mr Blair sound even more absurd.

2. The most significant point though was not the bonhomie. It was the fact that Messrs Cameron and Obama had clearly agreed a joint strategy to deal with the Lockerbie row. The PM promised that Gus O'Donnell, the Cabinet Secretary, would scurry around looking for any more information. And the president declined to push for a UK government inquiry. Not a bad strategy. Let's see if it works.

3. We have yet to see any evidence of David Cameron's much vaunted hard-headed approach to the alliance. This morning in the Wall Street Journal he was promising an end to blind loyalty and a greater British self-confidence. This afternoon he was falling over himself to suck up to Mr Obama. Pace: "I was so impressed by how tidy your childrens' bedrooms were"; or, "I believe our relationship can be win-win."

4. Pity Britain's ambassador to Germany. He will have to explain why David Cameron confessed that he was only able to cheer for Germany during the World Cup because he had been drinking Mr Obama's "very effective" beers. Cheering Germany was "a big admission for a British person", he said. Hmm. Diplomat Mr Cameron ain't.

I stand corrected. We are on the flight and the PM and his team have turned right and are slumming it in business class.

"Welcome to the new austerity," laughs an aide. They are spread out with nothing separating them from hoi polloi, at least those polloi who can afford business class.

The security is quite discreet. I wonder who is up in first class and whether they are feeling just a little sheepish? Or maybe they will just sit back in their wide seats, comfortable in the knowledge that they, unlike the prime minister, managed to wangle an upgrade?

For a Conservative, David Cameron is no respecter of tradition. The massed ranks of Westminster lobby correspondents heading for Washington would normally join the prime minister on a flight specially chartered for the occasion.

Yes, not quite Air Force One, but at least a plane of his own for Britain's head of government. Thus we could while away the Atlantic together, journalists and officials gossiping in relative comfort, briefing each other and fixing media pools.

If we were lucky, the PM would wander down the aisle at some point and we could chat off the record and pretend to be chums.

But no, not tonight. Mr Cameron has decreed that we shall all travel on a scheduled flight. He, of course, will turn left as he arrives on board; we shall turn right.

The aim is to let the voters know that, in these days of austerity, the prime minister himself is tightening his belt. And tightening ours at the same time.

The PM does not wish to waste money, we are told. Perhaps. But maybe he also does not wish to spend too much time trapped on a plane with the fourth estate. Ah well, we knew this special relationship could not last forever.