Deputy Prime Minister John Prescott has described the circumstances of Saddam Hussein's execution as "deplorable".
Saddam Hussein was hanged at the weekend
Mobile phone footage showed Saddam being told to "go to hell" by people attending the hanging, while the ex-leader mocks their "bravery".
Mr Prescott said those responsible for the scenes should be "ashamed", without saying if that included the Iraqi government which organised the hanging.
Iraq's government has now begun an inquiry into Saturday's events.
Mr Prescott told BBC Radio 4's Today programme: "I think the manner was quite deplorable really.
"Frankly, to get this kind of recorded messages coming out is totally unacceptable and I think whoever is involved and responsible for it should be ashamed of themselves."
Prime Minister Tony Blair, currently on holiday in Florida, has been criticised by Labour MPs opposed to the Iraq War for refusing to make an official statement about the execution.
Glenda Jackson branded his lack of public reaction "amazing", while Peter Kilfoyle said it was "yet another error in a long catalogue" on Iraq.
Downing Street said Foreign Secretary Margaret Beckett had spoken "on behalf of the whole government" when she gave her reaction to Saddam Hussein's death at the weekend.
She said Saddam had been "held to account", but added: "We do not support the use of the death penalty... we advocate an end to the death penalty worldwide, regardless of the individual or the crime."
The silent, official film released after the execution showed a subdued Saddam Hussein.
But the other footage, believed to have been filmed on a mobile phone, shows a charged, angry scene.
Unlike the official film, it shows the moment that the gallows trapdoor opens.
The amateur footage first appeared on websites and then excerpts began airing on major news channels.
The authorities fear the secret footage could contribute to a dramatic rise in sectarian tensions between Iraq's Sunni and Shia communities.
"There were a few guards who shouted slogans that were inappropriate and that's now the subject of a government investigation," an adviser to Prime Minister Nouri Maliki, Sami al-Askari, told Reuters news agency.
'Wrong to interfere'
The official line from UK government ministers has been that they oppose the death penalty - but say the decision to execute Saddam was one for Iraq's government to take.
The Bishop of Lichfield, the Rt Revd Jonathan Gledhill, said Saddam's hanging "cannot be called unjust".
In a statement, he added: "For many criminals death is in fact a greater mercy than life-long imprisonment... Anyone who deliberately murders another human being immediately forfeits his or her own right to life.
"If Saddam Hussein had a fair trial and proper opportunity to appeal, his execution cannot be called unjust."
The Archbishop of Canterbury, Dr Rowan Williams, had demanded a "sharp and unequivocal punishment" for Saddam but not death.
"I would say of him what I have to say about anyone who has committed even the most appalling crimes in this country, that I believe the death penalty effectively says there is no room for change and repentance," he told the BBC.