A British force has begun moving out of the southern Iraqi city of Basra in a move north to take over operations previously carried out by US forces.
Some 850 troops are being redeployed south of Baghdad
The 850-strong battle group led by the 1st Battalion The Black Watch is moving into an area south of Baghdad seen as among the most hostile in the country.
About 8,000 UK troops will remain stationed in southern Iraq.
The UK agreed last week to Washington's request for the redeployment, which has been controversial in Britain.
Critics say it is a political move ahead of the US presidential election - a charge denied by the government.
The group being redeployed will comprise three companies of armoured infantry from the 1st Battalion The Black Watch, with some 500 men and 50 Warrior armoured fighting vehicles.
They will be supported by a reconnaissance unit from the largely-Welsh Queen's Dragoon Guards, with around 100 men and 12 Scimitar armoured fvehicles, and a 50-strong Royal Marine light infantry unit from 40 Commando.
There will also be support troops including engineers, logisticians, signallers and medics.
The Black Watch, which traditionally recruits from Perthshire, Angus and Fife, is based in Warminster, Wiltshire.
BBC correspondent Ben Brown, in Basra, said the troops were aware of the controversy over the move but remained "proud to have been asked to do this mission, that they see it as a new challenge in a new part of Iraq".
He said: "They have seen quite a lot of action here and although it may be more dangerous where they are going, they say they are fully prepared for it."
In other developments:
The militant group led by Abu-Musab al-Zarqawi, which killed British engineer Ken Bigley, has threatened to kill a Japanese hostage if Tokyo fails to withdraw troops within 48 hours. Shosei Koda, 24, is thought have been sightseeing in Iraq
The Pentagon has confirmed it is considering boosting US troop numbers in Iraq. The extra forces would provide extra security in the run up to the Iraqi election, scheduled for January.
The area south of Baghdad where British troops are to begin operating includes towns like Mahmoudia and Latifiya.
From Baghdad, BBC correspondent Paul Wood said: "These are very, very tough places, with a mixture of nationalists, Baathists and Islamists very hostile to any coalition presence.
"They have put constant pressure on the American troops who are now leaving those locations to go to take part in the fight for Falluja."
Ben Brown suggested the British troops might adopt a "more restrained... more softly, softly style of soldiering" than the Americans they were replacing.
"They think that has got results down here in the south," he said.
"They think they have made more progress with the local community than perhaps the Americans have further north."
He added: "There is a suspicion that the Americans are too aggressive, too confrontational.
"They always wear helmets and big sunglasses; the British try to wear berets wherever they can and appear to be more friendly.
"Whether that will be a luxury in these towns like Mahmoudia and Latifiya, which are pretty lawless, pretty scary places... we will have to wait and see over the coming weeks of this mission".
Prime Minister Tony Blair has said the Black Watch will be home for Christmas.
But Ben Brown said that promise did not preclude other British troops from taking over from them, especially if the American marines, who they are replacing, run into difficulties in Falluja.