The draft also covers troops from Australia, Estonia, El Salvador, Romania and Nato.
Gordon Brown, Britain's prime minister, said last week that British troops would end their mission in Iraq by the end of May.
All but 400 soldiers will have left Iraq by the end of July, he said.
John Hutton, Britain's defence secretary, said that he expected the Iraqi parliament to have a deal in place by the end the year and said a strategy is in place if no bill is passed.
"We have contingency plans. The safety of our guys out there is our top priority. There will have to be an agreement, a proper agreement, before our guys are out on the streets."
At least 178 British soldiers have died in Iraq since the war began, including 136 in hostile incidents.
The presence of foreign troops in Iraq is authorised by a UN mandate which expires at the end of December.
On Saturday, lawmakers rejected a draft law that would have permitted their continued presence, arguing that foreign relations required not legislation but treaties or agreements with individual countries.
|Iraqi police and soldiers will take control of security in the country from 2009 [AFP]
Some politicians said that due to the lack of time, parliament was not likely to pass an interim resolution, a law, or even a memo allowing the forces to remain in Iraq until proper treaties or agreements were signed.
Under the draft law defeated last week, foreign forces would have to cease combat operations at the end of May and withdraw completely by the end of July, more than six years after the US-led invasion to topple Saddam Hussein, the former Iraqi president.
Lawmakers who rejected the bill did not appear to be opposed to the terms or the timetable established in the law, only to the format in which the withdrawal deal was framed.
They said they wanted a format similar to that in a US-Iraq bilateral security pact that allows 140,000 or so US troops in Iraq to stay for three more years.
As violence subsides, the deal highlights Iraq's growing control over its own security and the apparent reduced need for foreign troops.
From next year, Iraqi police and soldiers will take the lead in ensuring security in the country.
The US and Iraq have already signed a Status of Forces Agreement, which mandates the presence of US combat troops in Iraq until the end of 2011.
Parliament is set to reconvene on Tuesday.