Police said gunmen in a large convoy of vehicles typically used by police had sealed off streets round the building before making off with the hostages.
Iraqi Foreign Minister Hoshiyar Zebari says that a Shi'ite militia group loyal to radical cleric Muqtada al-Sadr was most likely behind the kidnapping.
Zebari said he suspected the Imam Al-Mahdi Army, which controls the area of Baghdad where the kidnapping took place.
The British Foreign Office said it was in urgent contact with the Iraqi authorities to try to establish facts and secure a swift resolution.
A British government crisis cell known as Cobra has been activated to plan a response.
Also on May 29, the U.S. military said 10 of its soldiers were killed in Iraq on May 28, including two in a helicopter crash.
At least 112 U.S. service personnel have been killed so far in May, making it the deadliest month for U.S. troops in Iraq in the past 2 1/2 years.
Meanwhile, two separate car-bomb attacks killed at least 40 people and wounded dozens of others in Baghdad.
(compiled from agency reports)