Kim Sengupta: An Afghan exit strategy will test this special relationship

William Hague's visit to Washington comes at a time when clarification is required from both sides on pressing international issues. The "special relationship" may still exist but it is not entirely clear what it means and the direction it will take.

The loosening of ties was inevitable after the era of Tony Blair's moist-eyed adoration of George W Bush ended. The rapport between Barack Obama and Gordon Brown hardly reached the same level, a situation embarrassingly highlighted last autumn when the Prime Minister had to pursue the US President around the UN building in New York to get a face-to-face photo opportunity.

The Tories have made much of the fact that Mr Obama was the first foreign leader to congratulate David Cameron on getting to No 10. But that has been the custom between the countries and it is hardly a sign that the US administration is going to focus on the UK with renewed energy.

There are, of course, areas of common purpose, nowhere more so than Afghanistan. Mr Hague said the war will be the focal point of his discussions with Hillary Clinton.

But there are differences between Britain and the US on the exit strategy. London has been pressing President Hamid Karzai to extend his dialogue with the insurgency even to those who show no sign of giving up violence. The US position is that the talks should only take place with those prepared to embrace the political process.

Washington also firmly holds that no meaningful exchange can happen until the Taliban have been militarily beaten, as far as that is possible in a counter-insurgency. President Karzai, smarting from the endless lectures by Western politicians on issues ranging from corruption to the Afghan security forces, has been quick to point out the Anglo-US split.

General David Petraeus and General Stanley McChrystal, the two most senior American commanders running the Afghan war, would like British forces to move from Helmand to neighbouring Kandahar next year. The transfer has the support of Lieutenant-General Nick Parker and Major-General Nick Carter, the two most senior British officers in Afghanistan, as well as some of their colleagues back in the UK. Until now, the Foreign Office and Downing Street have opposed the switch to the birthplace of the Taliban, which will bring with it more casualties and the possibility of the mission being prolonged.

The Americans are concerned by just how much influence the Liberal Democrats will have on the UK's foreign policy. Overwhelming numbers in the party want to pull troops out of Afghanistan and oppose to any military action to stop Iran's nuclear programme.

The pre-nuptial agreement which formed the coalition in Britain appears to rule out Liberal Democrat influence in these matters and Mr Hague insists Britain will stay the course in the Afghan war and that Iran must mend its ways or face consequences.