But in an admission that Britain's reputation as a world leader in counter-insurgency warfare has suffered a setback in Iraq and Helmand province, UK military chiefs will also take lessons from the Americans in how best to conduct "hybrid" operations that blend military and civilian power.
Under plans agreed as part of a White House review, Nato teams will try to peel away reconcilable Taliban supporters, many of whom are fighting Nato for money.
Local village elders will receive financial support for small scale local reconstruction projects and training for local security forces to convince militants to lay down their weapons. The move is designed to lessen Western reliance on the central government of President Hamid Karzai, which is widely regarded as irredeemably corrupt.
Britain has been asked by the Americans to use its experience in Afghanistan to convince other Nato nations to send their own civilian reinforcements to the Provincial Reconstruction Teams (PRTs) which will lead the reconstruction work.
A British diplomat said: "We are already practising some of what we are preaching. Our PRT in Helmand province has 80 civilians in it at the moment. Other comparable sized PRTs have just three or four civilians. That's out of about 200 people.
"There are discussions about rebalancing those and seeing how we can improve the civilian component. It's good to get development, security, economic policy and infrastructure under the umbrella of one coordinating body."
The Foreign Office is also working on how to bolster its own contribution alongside 300 new US civilians.
President Obama is expected to sign off on the strategy review, being drawn up by former CIA officer Bruce Riedel, this week before he travels to Britain for the G20 and Nato summits. The review will also detail plans for driving al-Qaeda and Taliban forces from the tribal areas of Pakistan, with controversial proposals for more intensive drone missile strikes across a broader area of the border region.
Both Britain and America have abandoned hope for securing any significant increase in combat power from the rest of Nato and are focusing instead on shaming other Nato nations into joining the soft power offensive.
But Britain also hopes to learn from the Americans. In a frank briefing after his meeting with Mr Gates, Mr Hutton admitted that the British armed forces have had to concede they have lesssons to learn from the US in conducting counterinsurgency operations, in which UK was once regarded as a world leader.
Mr Hutton insisted that he had heard nothing but praise for the contribution of British troops from Mr Gates, the US defence secretary, and senior US officers, but admitted that there had been background grumbling from middle ranking US officers who believed that British commanders abandoned Basra to Islamic militias and lost ground in Afghanistan.
Mr Hutton rejected as "unfair" claims that Britain's contribution to Iraq and Afghanistan has not been worthwhile.
He said: "It's not a criticism that's ever been put to me but I've heard it swirling around. I'm aware of it but I think it's at a lower level. It is unfair.
"The Afghan mission would be in a lot more trouble if we were not there. If I had a meeting with Gates and he said: 'Look you guys are just crap, you've done nothing and you're no use to us at all, it would be a different story.'"
But the defence secretary said that the British military had "always been very ready to learn."
Part of his discussions with Mr Gates involved finalising plans for the US to work with the British military to develop new capabilities to be able to conduct "hybrid" operations in the future.
Mr Hutton said: "The campaign in Afghanistan is a good example of it, trying to do the civil effect alongside the military effect, stabilisation. The Americans have done a lot of work on this. We want to learn as much from them as possible."
The agreement will see senior British officers work alongside Americans to develop some "new thinking, new strategy, possibly some new equipment, new tactics for enabling the British Army to conduct these kind of operations more successfully in the future."
Ministers are still deciding whether to increase the number of British combat troops. President Obama has not requested a further battalion but Army chiefs have indicated that between 1,000 and 2,000 extra soldiers could be forthcoming.
Mr Hutton added: "We share a very similar analysis of the problem and what we need to solve it. We need more security on the ground. We need greater civil effect, that's where I think Europe needs to do more.
"The Taliban and al-Qaeda have been hit extremely hard in the last two or three years. They're hurting. There's no doubt at all that there are parts of that network that are ready to talk. It is possible to peel away from the Taliban insurgency the people we can do business with."