The Prime Minister faces mounting calls from within his party to draw down the remaining 4,100 troops in Basra and bring the soldiers home.

A series of amendments has been tabled for next weekís National Policy Forum demanding immediate troop withdrawal. But a report to be published by the Commons defence select committee also next week will urge ministers not to bow to political pressure and ìcut and runî from Iraq.

Speaking during a visit to British troops in Baghdad yesterday morning, the Prime Minister insisted he would not publish an ìartificialî timetable for withdrawal.

But privately ministers and officials are becoming increasingly bullish about the prospects for the withdrawal of the bulk of Britainís remaining 4,100 troops in Iraq ñ probably around the end of next year or early 2010.

Downing Street sources insist they are relaxed about Barack Obamaís controversial plan to withdraw American troops from Iraq by June 2010 if he wins the US elections in November this year.

Yesterday Obama was in Afghanistan, where he met the commander of US troops in the east of the country.†

A senior source said Mr Brown was ìworking to the same endî as the Democratic candidate, who will hold talks with the Prime Minister during a visit to London this week.

Although a final decision on withdrawal will depend on conditions on the ground, the source hinted that the Government hopes to pull out the bulk of British troops ahead of the Obama timetable.

He added: ìThe Americans are in a different position to us. We are already in Overwatch mode, concentrating on training Iraqi forces, and we have seen excellent progress in the south in recent months.î

The Prime Minister will lay out four key milestones that have to be achieved before withdrawal is possible, and Downing Street and the Army believe they are all on course.

The objectives are the training of local army and police; local elections being held; economic and social development in the Basra area; and the transfer of Basra airport to civilian use. ìThese are the building blocks for the future. It is absolutely essential that we complete these tasks,î Mr Brown said.

ìI am not setting an artificial timetable, but what I can say is there has been significant progress in all these areas.î

The Prime Minister said there had been a ìturning pointî in the violence in recent months, with the number of incidents reducing dramatically since he was last in the country. ìIn a period of six months enormous progress has been made,î he said.

Mr Brown spent just under an hour at Nouri al-Malikiís offices, speaking to the Iraqi Prime Minister and later President Jalal Talabani before being joined by advisers.†

Mr Brown said he had agreed to hold further talks with Mr Maliki in the autumn.

The head of Britainís armed forces, Chief of Defence Staff Air Chief Marshal Sir Jock Stirrup, this week said he expected a ìsubstantial change in our mission in Iraqî early in 2009 and was ìconfidentî of a reduction in the UK commitment over the course of next year.

Plans to reduce the British contingent to about 2,500 by spring had to be postponed earlier this year because of an increase in fighting around Basra.

The Prime Minister was last night due in Jerusalem to hold talks on the Middle East peace process.