"It's not really helpful to speculate at the moment but as security improves and Iraqi forces improve their capabilities, which they are doing daily, then obviously there's scope for numbers to be reviewed."
Maj Gen White-Spunner added there was an "overwhelming feeling of optimism" in Basra.
Gordon Brown told MPs before the summer recess the 4,100 UK troops currently deployed in Iraq would stay "for the next few months".
He said there had been a "marked improvement" in conditions in Basra and the focus of British armed forces was to complete the task of training and mentoring the 14th Division of the Iraqi Army.
But in the first few months of 2009 there would be a "fundamental change of mission" to "make the transition to a long-term bilateral relationship with Iraq", he added.
Conservative MP Bernard Jenkin, who recently visited Basra as part of the Commons Defence Select Committee, welcomed the indication but said it was important not to "undermine confidence" by announcing withdrawals too soon.
He added there was also an opportunity for the UK to maintain a military training and mentoring role for years to come "in a country that is going to become extremely wealthy and important in the region where our influence will be very beneficial".
A Ministry of Defence spokesman said although it was hoped the UK military presence in Iraq would decrease "significantly in the future", it was too early to discuss the "size and shape of a reduced UK forces' footprint".
The change of mission would be based on conditions on the ground, the plans of coalition partners and the military contribution requested by the government of Iraq, he said.
The US was "intimately involved" with the development of future plans and was "fully supportive" of the UK's current position and proposals, he added.
Liberal Democrat foreign affairs spokesman Edward Davey said it appeared the troops were there "more as political cover for the Brown-Bush relationship than to provide any real help to the Iraqi people".
The government was wrong not to set out a clear timetable and troops should be withdrawn by Christmas this year, he added.
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