They are expected to pull back to the vast British airbase on the outskirts of the city.
It has long been expected that the British would withdraw its small, vulnerable garrison from the city and consolidate at the airport.
The withdrawal means the end of a British presence in the city for the first time since the US-led invasion that toppled Saddam Hussein in 2003.
The Sunday Times newspaper has reported that Britain is preparing to hand over control of Basra province to the Iraqi army as early as next month, enabling most of the 5,500 British soldiers to leave Iraq.
US policy criticised
The Basra withdrawal comes amid condemnation by a second former UK army chief of the US for its "fatally flawed" policy in Iraq.
Major-General Tim Cross, the most senior UK officer involved in post-war Iraq planning, told the Britain's Sunday Mirror he had been "very concerned" about the lack of detail that had gone in to plans to rebuild Iraq after the invasion.
|Maj-Gen Jackson has criticised US handling of|
Iraq's post-war reconstruction [Getty Images]
He said Donald Rumsfeld, the former US secretary of defence, had dismissed concerns regarding the lack of sufficient troop numbers to maintain security and assist in Iraq's reconstruction.
"He didn't want to hear that message. The US had already convinced themselves that Iraq would emerge reasonably quickly as a stable democracy.
"Anybody who tried to tell them anything that challenged that idea - they simply shut it out."
The remarks by Cross follow those of General Sir Mike Jackson, head of the British army during the Iraq war, who criticised the US for how Iraqi reconstruction was handled.
However, the generals' criticism has been rejected by John Bolton, former US ambassador to the UN.
Speaking on a BBC programme, he said that Jackson's remarks "read into a version of history that simply is not supported by the evidence".
Bolton said: "I'm not saying that we got it right in Washington because I've made my own criticisms. His [criticisms] just happen to be way off the mark, very simplistic [and] I think in a sense limited by the role that he had."