I cannot look at British Prime Minister David Cameron without feeling that he has been made from an Identi-Kit, and that they just missed the perfect likeness. The hair is from a Vidal Sassoon catalogue; the face from an exhibition of Dutch masters; and the body from, well, the ranks of the well-fed but not fat.

This sense that Cameron is a made-up man came back to me in the East Room, when President Barack Obama welcomed him to the White House as both men gave their first joint press conference since the prime minister was elected.

With just four questions from pre-selected reporters, it is stretching it to call these events press conferences; and the lack of enthusiasm for the format was shown by the empty media seats.

Anyway, the purpose of the event was to convince the media that Cameron and Obama are on the same page of the hymnal. Everybody knows they are not. They are divided by four not-unsubstantial issues.

They tried hard to sound like chums. They wore almost identical dark suits and blue ties. They called each other by their first names: It was “David” this and “Barack” that.

There has been a steady growth of informality at the White House, but this was a new mile post. One British reporter -presumably for the benefit of his American colleagues -actually addressed Cameron as “Mr. Prime Minister.” That is a form of address peculiarly American and never heard around the British Parliament. The British prefer to believe that a title determines the form of address. So it is simply, “Prime Minister, could you tell us …”

Cameron tried to set the stage by writing an article that appeared that morning in the Wall Street Journal. In it, he redefined the “special relationship” and called for the British to be less sentimental about it.

Underlining their differences, Cameron and Obama share something that is not helpful: neither of them is an Atlanticist.

Unlike many British Conservatives, Cameron has not been seduced by the United States. He did not spend a year at a U.S. university and has not peppered his talk with mention of the American example.

Likewise, Obama is one of the least Eurocentric of American presidents. He, too, did not spend time at a British university, as did Bill Clinton. He even offended many by banishing a bust of Winston Churchill from the Oval Office.

We do not know whether the public coziness extended into two days of talks between Obama and Cameron, but the policy differences are wide.

First, there is the global economy. Obama and his advisers believe too much austerity now will lead to a second recession and catastrophic deflation. So much so that Obama wrote to his partners in the G8 urging them to stimulate, not strangle, their economies.

But Cameron, keenly aware of the fate of Greece and the downgrading of Irish debt, has put forward an austerity budget and asked his departments to come up with possible cuts in staff and expenditures of 25 and 40 per cent, respectively. The real pain will not be felt until the cutting begins in the fall.

Second, there is the delicate matter of BP. Obama does not mind if the oil giant is squeezed so much over the disaster in the Gulf of Mexico that it has to be sold off to, say, an American company. Cameron minds a lot.

Then there is the release of Abdel Baset al-Megrahi, the Lockerbie bomber, by the Scottish government. Americans want an inquiry into whether there was a deal to release al-Megrahi to protect British business interests in Libya, possibly involving BP. Cameron, who opposed the release at the time, thinks it is a closed issue. But he has already been pressured into a review.

Finally there is the case of Gary McKinnon, the computer genius with Asperger’s syndrome, who hacked into Pentagon and NASA computers after 9/11. The United States wants him extradited for trial here and Cameron is under pressure on grounds of humanitarianism and sovereignty not to oblige. Obama says it is a legal not presidential matter; Cameron raised it anyway.

His “special relationship” might not be Obama’s cup of tea.