Most Americans will probably pay little attention to the prime minister’s visit to the United States this week. Unlike Tony Blair, Gordon Brown is a relatively unknown figure outside Wall Street and Washington.

For the White House, however, Brown’s trip is important, coming at a sensitive time in US-British relations against a backdrop of mounting tensions over the war in Iraq. There is a looming crisis in the special relationship that neither Washington nor London will openly acknowledge.

For the Americans, Brown is probably the least-liked British leader since Edward Heath. There is a growing sense in the executive branch, from the Pentagon to the West Wing, that Brown has adopted a complacent, laissez-faire approach to the Anglo-American alliance and is indifferent to its long-term fate.

There is a firm belief in the military that the prime minister is running Britain’s armed forces into the ground, refusing to spend the necessary money on rebuilding their power, undercutting the fighting ability of America’s closest partner.

Above all, Brown is seen as lacking the stomach for what many US political leaders and strategists see as a global war against Islamist terrorism, and is viewed increasingly as a half-hearted and unreliable partner.

He is also perceived as far too willing to submerge British power within the United Nations, the European Union and other supranational organisations, following consensus rather than leading and taking difficult decisions that may offend Britain’s European neighbours.

It has not gone unnoticed that since Brown took charge, the British embassy no longer uses the term “special relationship”, and that the Anglo-American alliance has been downgraded to Britain’s “most important bilateral relationship” in deference to Brussels.

The divide between the British and American approaches is strikingly illustrated in Iraq, where over the past 15 months Washington has “surged” tens of thousands of extra troops into the country, stepping up military operations with considerable success against Al-Qaeda and Sunni terrorist groups. London in contrast has steadily reduced the British military commitment, cutting troop numbers from 7,100 to 4,100, pulling British forces out of Iraq’s second city Basra last September. This prompted John McCain, the Republican presidential candidate, to criticise the British strategy in March.

In last month’s battle for Basra between Iraqi security forces and Iranian-backed Shi’ite militias led by Moqtada al-Sadr, US aircraft bombed enemy positions, and hundreds of American troops joined the ground offensive in a part of Iraq that Britain had dominated for almost five years. However, British forces remained largely on the sidelines, apart from limited logistical support and shelling of militias’ positions.

Downing Street rightly decided to halt the further withdrawal of 2,500 troops from southern Iraq, but there is little sign that Brown plans to put British battle groups into action if the temporary ceasefire ends.

Unless there is a reversal of London’s approach, the US is likely to have to deploy thousands of troops from the Sunni heartlands around Baghdad to the south to take on the militias and ward off Iranian influence.

The Anglo-US divide is also on display in Afghanistan, this time not over troop numbers (with 8,000 British troops on the ground) or Britain’s willingness to fight, but over big-picture tactics in waging the war against the Taliban.

Des Browne, the defence secretary, recently caused alarm in Washington with his ill-judged remarks in a newspaper interview on counter-terror strategy. Browne urged direct talks with sections of the Taliban as well as with Hezbollah, representing a marked shift away from the government’s earlier position of “no negotiations with terrorist groups”.

Browne’s remarks followed the revelation that the British government had secret plans for building military training camps for former Taliban fighters in Helmand province, a move that was fiercely condemned by the Afghan government in Kabul.

The different approach to the Afghanistan mission underscores a deeper gulf between the allies in interpreting the nature of the conflict. From Washington’s point of view, the free world is engaged in a long war against Islamist terrorists that may take generations to win, that will require significant sacrifice and a massive military commitment. As the recently released British national security strategy shows, London’s view is significantly different, with its declaration that terrorism “does not at present amount to a strategic threat”.

It is an unfortunate reality that the US and Britain are beginning to drift apart at a critical moment when both countries are engaged in wars in the Middle East and south Asia, and must also confront the threat of a nuclear-armed Iran and a belligerent Russia.

It is not, however, an irreversible trend. For both Washington and London, protecting and defending the special relationship should be a top priority. For either side there is no realistic alternative.

The Anglo-American alliance has been the most successful partnership of our time. The relationship has to operate as a two-way street. As he goes to Washington this week, Brown must demonstrate Churchillian mettle, and show that Britain is willing to pull its weight alongside its closest ally.

Nile Gardiner is a director at the Heritage Foundation in Washington

Times Recommends

• Five golden rules for regulating banks
• Uighurs’ cry echoes round the world
• It is not just democracy that is illegal