'More' UK troops to withdraw from Afghanistan in 2011
More British troops than expected could be brought home from Afghanistan this year, Ministry of Defence sources say.
David Cameron has already said about 400 troops will be withdrawn, although the overall level will stay at 9,500.
But the BBC's Carole Walker has been told there will be a fresh assessment in July and it could result in greater numbers returning to the UK.
On Wednesday US President Barack Obama announced 10,000 US troops would be withdrawn in 2011.
That will be followed by a further 23,000 by the end of September 2012, with 68,000 to remain for now.
French President Nicolas Sarkozy said France would begin to withdraw 4,000 soldiers.
The British military has the second largest number of troops in Afghanistan after the US - current force levels are 9,500.
The prime minister has said UK forces will withdraw from combat roles by the end of 2014 and that about 400 troops would be withdrawn in the year to February 2012.
Mr Cameron welcomed President Obama's announcement: "The surge by the US and international partners, supported by an increase in the number of Afghan army and police, has reversed the momentum of the insurgency and created the right conditions for security responsibility to begin to transfer to the Afghans from July.
"We will keep UK force levels in Afghanistan under constant review. I have already said there will be no UK troops in combat roles in Afghanistan by 2015 and, where conditions on the ground allow, it is right that we bring troops home sooner."
He added the UK would work with Afghanistan and others to achieve a "military and political solution" in Afghanistan.
Defence sources have suggested that, following President Obama's speech, the National Security Council will meet over the next few weeks to look at whether it is possible to bring home more troops than announced over the course of this year - although it is understood it would be unlikely to be large numbers.
Foreign Secretary William Hague, who is visiting Afghanistan, told BBC Radio 4 there had been in contact with the Taliban as part of efforts at "political reconciliation", and Britain was "connected to that and supportive of that".
He told the Today programme: "It is the case that efforts to arrive at a political reconciliation in Afghanistan must run alongside our military efforts and indeed the military efforts - the improvement of security on the ground - are part of keeping up the pressure for such a reconciliation to take place."
While there was more to do in security and reconciliation, as well as making economic progress and fighting corruption, he said he had seen "positive changes" in Lashkar Gah, which he visited during a joint trip with the foreign minister of the United Arab Emirates, Abdullah bin Zayed al-Nahyan.
"Undoubtedly there will be difficulties ahead, but the confident Afghan security leadership I was able to witness is greatly encouraging, not only for Afghanistan's security but also for our own," he said.
In a BBC documentary the head of the British Army, General Sir Peter Wall, appeared to question the 2015 deadline for withdrawing British troops.
While he stressed that the Army was "committed to deliver against that deadline" he added: "Whether or not it turns out to be an absolute timeline or more conditions-based approach nearer the time, we shall find out".
But his predecessor, Lord Dannatt said his comments had been taken out of context. He told the BBC: "Undoubtedly conditions on the ground are really important to guide what the military does, but the government of the day has made it quite clear that by 2015 our combat operations will have ended.
"That's the government's decision. Peter Wall understands exactly what I am saying, that this situation is essentially one with a political outcome. Of course conditions on the ground determine the speed at which you can do things, but it's been made quite clear that we will have stopped our combat role by 2014-2015."
The Taliban has said more serious steps than those outlined by President Obama were needed "to stop this pointless bloodshed".
In a statement issued to the media, it said: "The solution for the Afghan crisis lies in the full withdrawal of all foreign troops immediately and (while) this does not happen, our armed struggle will increase from day to day."
The US currently has about 100,000 troops in Afghanistan overall.
Divisions remain within the Obama administration over the size and speed of the pullout.