Gordon Brown should be worried about today's meeting between David Cameron and President George W Bush, even if it is officially described as a "drop in".

Cameron is being granted a rare visit for an opposition leader with the US president, the first for a Conservative Party chief since 2001. Such audiences are usually only reserved for foreign politicians with a distinguished record, who have a significant personal connection to an American administration (as was the case with Iain Duncan Smith), or who are seen as potential leaders-in-waiting.

With the Conservatives up to 13 points ahead in the polls, they are now credible contenders to seize the reins of power from Labour, and Washington is taking notice.

The fact that Cameron is being welcomed in the White House speaks volumes about the increasingly frosty state of relations between Downing Street and the Bush Administration. An invitation to a Conservative Party leader would have been unthinkable just a year ago.

The heady days of the Bush-Blair era, with its extraordinarily close-knit partnership, are however long gone, as are American hopes of rekindling it with Brown. The Prime Minister rarely speaks to the American president on the phone, and their first meeting in July was businesslike but underwhelming. While Blair wowed Washington's policy elites on a regular basis, Brown has largely bored them.

The Prime Minister's foreign policy appointments have also raised eyebrows on this side of the Atlantic. His elevation of the fiercely anti-American Mark Malloch Brown as the new Minister for Africa, Asia and the United Nations was a public relations disaster that sent a chill through the Special Relationship.

Malloch Brown has already overshadowed the far less experienced David Miliband, who has hardly set the world alight as Foreign Secretary.

The vast majority of Americans have no idea who Gordon Brown is, but a sizeable chunk could identify French President Nicolas Sarkozy, who was all over American TV screens recently with a glamorous speech to Congress and a genuinely warm tête à tête with President Bush in the Oval Office.

In the space of a few months, Sarkozy has outclassed his British counterpart, and the charismatic French leader is emerging as the most powerful figure in Europe. It is pretty embarrassing when Britain gets edged aside in the affections of the American public by, of all people, the French. And all this when Paris has barely offered anything concrete on the table, while more than 12,000 British troops continue to fight bravely in Iraq and Afghanistan.

It is against this backdrop that David Cameron has been given an important opportunity to make a name for himself on the international stage. It is also a chance to repair some of the damage caused by Shadow Foreign Secretary William Hague's speech to the Royal Institute of International
Affairs which referred recklessly to a "solid but not slavish" alliance, and called for "the effective management of the relationship with the United States of America".

A few months earlier, Cameron chose the fifth anniversary of the 9/11 attacks to call for the need for "humility and patience" in conducting foreign policy, comments that were interpreted in Washington as a direct attack on US leadership of the war on terror. These were not the words of a government in waiting, but insensitive attacks on Britain's closest ally and friend.

There is no bigger setting in international affairs than Washington, and it is important that Cameron projects the qualities of a potential future prime minister, and avoids the kind of knee-jerk anti-Americanism that has become all too common in today's Conservative Party.

There will clearly be disagreements with the US administration, but such disputes should be handled in private discussions and not exploited in order to play to a domestic gallery.

His message in the United States should be unequivocal - that British Conservatives are committed to defending and advancing the Anglo-American Special Relationship, and that the US and Great Britain must remain united in confronting Islamist terrorism and state sponsors of global terror. He must also show leadership over the Iranian nuclear crisis, the biggest threat to international security of our generation. Until now, Cameron has been largely silent on the issue, giving few clues as to how a Conservative administration would deal with the Mullahs of Tehran.

If David Cameron is to walk in the footsteps of Margaret Thatcher and Winston Churchill, there remains a mountain to climb for the Conservative Party leader. He must establish himself as a serious statesman firmly addressing the biggest global issues of the day, from Mahmoud Ahmadinejad's threats to wipe Israel off the map, to the continuing genocide in Darfur. He must also place the alliance with the United States at the heart of British foreign policy, for the world is a far more dangerous place when London and Washington are divided.

This is a high-stakes trip for Mr Cameron, but also an opportunity to demonstrate a truly conservative vision for British foreign policy.

Nile Gardiner is the director of the Margaret Thatcher Center for Freedom.