The deployment came hours after Iraq's most feared militant group released a video threatening to behead a Japanese captive within 48 hours unless Japan withdraws its troops from Iraq.
British Lt. Col. James Cowan said British troops, accompanied by 40 U.S. Marines, left the southern city of Basra to head for a base located north of Hillah, about 60 miles south of Baghdad. Forty U.S. Marines were with them, he said.
Associated Press Television News footage showed large flatbed trucks carrying armored British vehicles up a road through Iraq's southern desert.
In other developments:
The British soldiers' families expressed worries Wednesday that the redeployment puts the troops in greater danger.
"It wasn't a cake walk in Basra but it's going to be a lot, lot more dangerous up there," said James Buchanan, 56, from Arbroath in central Scotland, who has two sons with the regiment in Iraq. "They're going to get one hell of a kicking this time," he said.
Nearly 800 Scottish soldiers of the First Battalion, Black Watch are to replace U.S. forces who are expected to take part in offensives against insurgent strongholds west and north of the capital in an attempt to bring order to Iraq before elections in January.
The American military wants the British to assume security responsibility in areas close to Baghdad, so U.S. Marines and soldiers can be shifted to insurgency strongholds west of the capital, including Fallujah.
Prime Minister Tony Blair's decision to agree to the U.S. request for redeployment is a politically sensitive one for the British leader, whose popularity has plummeted because of his support for the Iraq war.
Britain's 8,500 troops are based around the southern port city of Basra in a relatively peaceful area of Iraq. Sixty-eight British soldiers have been killed in Iraq, compared with more than 1,000 U.S. troops.
Interim Iraqi Prime Minister Ayad Allawi said Tuesday that more extremists are massing in Fallujah and warned of increasing terrorist attacks to come.
In the hostage drama, a video was posted on a militant Web site Tuesday said a Japanese man was kidnapped by Jordanian-born militant Abu Musab al-Zarqawi's group and vowed to kill him within 48 hours unless the demands were met.
Japanese Prime Minister Junichiro Koizumi rejected the demands.
"The Self-Defense Forces will not withdraw," Koizumi told reporters in western Japan. "I cannot allow terrorism and cannot bow to terrorism."
The captive spoke briefly in halting English and Japanese, addressing himself to Koizumi.
"They asked me why Japanese government broke the law and sent troops to Iraq," the man said in English. "They want Japanese government and Koizumi prime minister, they want to withdraw the Japanese troops from Iraq or cut my head."
He then paused, sighed and switched into Japanese.
"Mr. Koizumi. They seek the withdrawal of Japanese Self-Defense Forces... (and say they) will take my head off," the captive said. "I'm sorry. I want to return to Japan again."
The video's authenticity could not be independently confirmed, but the Japanese government later identified the captive as 24-year-old Shosei Koda.
Tokyo has dispatched some 500 troops to the southern Iraqi city of Samawah on a humanitarian mission to purify water and rebuild schools in support of U.S.-led reconstruction efforts.
Foreign Minister Nobutaka Machimura urged the hostage-takers to immediately release Koda, saying that he had nothing to do with Japan's deployment in Iraq.
"Mr. Koda is a private individual who is not related to the Self-Defense Forces or the government of Japan," Machimura said.
When the captive finished speaking, the video showed him kneeling before three masked militants. One of them read a statement calling the man "an element attached to the Japanese armed forces."
"We give the Japanese government 48 hours to withdraw its troops from Iraq, otherwise his fate will be the same as that of his predecessors, Berg and Bigley and other infidels," the man said, referring to the beheadings of British engineer Kenneth Bigley and U.S. businessman Nicholas Berg.
The video, which lasted just under three minutes, bore the logo of al Qaeda in Iraq, the new name for al-Zarqawi's group, which was previously known as Tawhid and Jihad and has allied itself with Osama bin Laden. The group has claimed responsibility for the beheadings of Bigley, two American co-workers and Berg, as well as numerous car bombings and other attacks.
The United States has offered a $25 million bounty for the capture or killing of al-Zarqawi, who is believed to be hiding in the militant stronghold of Fallujah.