Britain's most senior military commanders have warned Gordon Brown that unless he sends more troops to Afghanistan Britain will lose credibility with its American allies, The Independent has learnt.

Senior generals are bemused that the Prime Minister has turned down the advice of his own Defence Secretary, John Hutton, that a larger force should be sent to Afghanistan following the withdrawal from Iraq. Now they have warned Number 10 that the reputation of the armed forces will suffer in the eyes of senior American commanders unless Mr Brown authorises an autumn surge in troop numbers. Such a surge, they say, would signal Britain's intent to "pull its weight" in the Afghan conflict by plugging the shortfall in the multinational force.

On Saturday, two more British troops died in Helmand, bringing to 165 the total number killed in the conflict so far – just 14 fewer than the total number of British soldiers who died in Iraq.

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Mr Brown has until now turned down, on cost grounds, the generals' proposal to send 2,500 extra troops in support of the projected US-led "surge" against the Taliban. Instead, he has authorised a deployment of 700 temporary troops to cover the period of the forthcoming elections in that country. But The Independent has learnt that defence chiefs have persuaded the Government to review the situation in the autumn. Even then, any increase is likely to be in the hundreds rather than in the numbers that the Army believes are needed.

In a sign of the private concern felt by senior military personnel over the Government's stance, General Sir Richard Dannatt, the head of the Army, has publicly warned that Britain's strategic alliance with US is at risk unless British forces are seen to be pulling their weight in Afghanistan.

In a speech to the international relations think-tank Chatham House he said: "Britain's calculation has long been that maintaining military strategic 'partner-of-choice' status with the United States offers a degree of influence and security that has been pivotal to our foreign and defence policy. But this relationship can only be sustained if it is founded on a certain 'military credibility threshold'.

"Credibility with the US is earned by being an ally that can be relied on to state clearly what it will do and then does it effectively. And credibility is also linked to the vital currency of reputation." General Dannatt added that "unfairly or not" British performance in Iraq and Afghanistan has already been called into question by some in the US administration.

"In this respect there is recognition that our national and military reputation and credibility, unfairly or not, have been called into question at several levels in the eyes of our most important ally as a result of some aspects of the Iraq campaign," he said.

"Taking steps to restore this credibility will be pivotal, and Afghanistan provides an opportunity."

This view has been backed up Col David Kilcullen, a former Australian army officer who helped plan General Petraeus's surge in Iraq and acted as an advisor to Condoleezza Rice.

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He told The Independent: "It is true that the British have received some criticism in the US, and some of it has been unwarranted. The Americans too made mistakes in Iraq, but they subsequently tried to rectify that.

"The British have a great opportunity to win back the credibility they have lost with the Americans and enhance it in Afghanistan."

Col Kilcullen, who remains close to senior figures in the US military, said that in his opinion the British General Sir David Richards, who is due to take over from General Dannatt as head of the Army, was "one of the best ever" head of Nato forces in Afghanistan.

He added: "No one doubts the professionalism and bravery of the British, and we accept that they already have a large force in Afghanistan. But we are coming to a crucial time in the campaign there, and I am sure more British help will be welcome."

The US is dispatching up to 17,000 troops to southern Afghanistan, with many of them going to Helmand, which is the centre of UK operations in the war. British commanders are convinced that after three years of committing resources and lives to the mission, reinforcements are essential to maintain the British footprint on the ground.

President Barack Obama is believed to have discussed additional troops for Afghanistan with Mr Brown. US commanders have also expressed disappointment at the shortfall in the troops being sent, especially after redeploying 4,000 troops from Baghdad to Basra to make up for the UK withdrawal from Iraq.

The Afghan campaign

8,300 British troops in Afghanistan

700 extra British troops deployed temporarily for election

610 British troops hurt from 1 January 2006 to 15 March 2009

175 British troops seriously injured between 1 January 2006 and 15 March 2009

165 British troops have lost their lives

39 British troops died in 2006 after taking over in Helmand

28 British troops killed in 2009

10 British troops seriously injured between 7 October 2001 and 31 December 2005