"Now that we know the full picture of what happened I think we can sum this up as a deplorable set of events," Brown said. "It is something, of course, of which the Iraqi government has now expressed its anxiety and its shame at. It has done nothing to lessen the tension between the Shia and Sunni communities."
A mobile-phone video showed observers taunting Hussein with shouts of "go to hell" and chanting the name of a Shi'ite cleric before the former Iraqi leader fell through a gallows trapdoor.
The images provoked international criticism and further inflamed sectarian passions in Iraq. Iraqi Prime Minister Nuri al-Maliki has pledged to investigate the way the hanging was conducted.
Brown, who is expected to take over as premier when Blair steps down this year, said he was pleased with the inquiry.
"I am pleased there is now an inquiry into this and I hope that lessons in this area will be learned, as we learn lessons in so many other areas about what's happened in Iraq," Brown said.
U.S. President George W. Bush has also said Saddam's hanging should have been carried out in a "more dignified way" but argued that he received justice, unlike his victims.
Brown himself flew to Iraq in November to visit British troops stationed in the south of the country.
He faces a tough challenge stepping into Blair's shoes. The Labour government has been undermined by the war in Iraq and is beset by scandals, while the opposition Conservatives have revived their fortunes under youthful leader David Cameron.
Iraq Violence Continues
Meanwhile, hundreds of Sunni Arabs protested today the execution of Hussein outside a Shi'ite shrine in northern Iraq. They marched through the streets of Samarra, where they gathered outside the Al-Askari mosque.
The Iraqi military reportedly killed 30 militants in a gun battle in Baghdad. In separate incidents, six other Iraqis died in Baghdad, and two others in the town of Hilla.
Earlier, 27 bodies of torture victims were found in the capital.
An Iraqi Education Ministry official escaped an attempt on his life in central Baghdad today. Police said that a roadside bomb went off near the convoy of Habeeb Abdul Hussein al-Shemari, director general of the ministry.
"We were sitting inside the shop, when a roadside bomb went off near this vehicle," an eyewitness named Seif told Reuters television. " We have two martyrs. The blast shattered all the windows of the shop and the belongings [of the shop] went upside down. It was a roadside bomb that went off near a vehicle."