Foreign Secretary Margaret Beckett said the hanging of former Iraqi President Saddam Hussein meant he had been "held to account" for his crimes.
Margaret Beckett said she spoke for the UK government
"I welcome the fact [he] has been tried by an Iraqi court for at least some of the appalling crimes he committed against the Iraqi people," she said.
But she said the British government remained opposed to the death penalty.
Liberal Democrat leader Sir Menzies Campbell said Saddam's death did not "make an illegal war legal".
He also said the execution would also not "put an end to the violence and destruction".
Sir Menzies said: "Saddam Hussein's death does not vindicate in any way the ill-conceived and disastrous decision to invade Iraq.
"Britain's interests will best be served by the withdrawal of our forces sooner rather than later."
Shadow Defence Secretary Liam Fox said Saddam had "faced justice".
"The verdict and sentencing of Saddam is a matter for Iraqi law and for the Iraqi justice system," he said.
"Saddam has now faced justice. We hope that Iraqis will now look to the future.
"However, there still remains a long way to go before Iraq becomes a stable country, in which security prevails."
Saddam and two co-defendants were sentenced by an Iraqi court for the 1982 killings of 148 Shias in Dujail.
"The British government does not support the use of the death penalty, in Iraq or anywhere else. We advocate an end to the death penalty worldwide, regardless of the individual or the crime," added Mrs Beckett.
"We have made our position very clear to the Iraqi authorities, but we respect their decision as that of a sovereign nation."
She said Iraq continued to face "huge challenges".
Leader of the Respect party, George Galloway, who met Saddam Hussein several times before he was deposed, said the former Iraqi leader's death could spark further violence in the troubled country.
He said: "He has been killed, but I believe he will be more dangerous to the forces of the occupiers and their allies after his death than when he was alive.
"I believe a wave of attacks will be carried out against those allied with the occupation."
Speaking before the execution, which took place just before 0300 GMT (0600 local time), Archbishop of Canterbury Dr Rowan Williams told the BBC that Saddam deserved "sharp and unequivocal punishment".
"But 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."
One UK-based Iraqi man, whose brother has been missing since being arrested under Saddam's regime in 1982, said the former dictator's execution would bring a sense of "release" to many people.
Jabbar Hasan, director of the UK-based Iraqi Association, said his death may also help Iraq to move on and rebuild.
Saddam Hussein was sentenced to death after a year-long trial
"He has got the punishment that he deserves for the crimes that he committed.
"Because of what the country has been through in the last 18 months people are not in the mood to celebrate but it will be a great release for many people."
Mr Hasan, a Kurd from Baghdad who now lives in Putney, south-west London, said Saddam was one of the people who had led the country to its current catastrophe.
Meanwhile, some families of British servicemen serving in Iraq have expressed fears that troops would become the target of a backlash in the wake of the execution.
Rose Gentle, whose 19-year-old son Gordon was killed in Iraq, said: "We are actually pretty frightened that it's going to cause a lot more trouble and that by executing Saddam we are going to make matters a lot worse."
"We know he is an evil person and that he has killed a lot of people but they should just imprison him because it is our boys who are going to suffer."
The Ministry of Defence said no specific precautions had been put in place in readiness for a backlash against British troops, but the security situation would be monitored.
"We will be keeping a mindful eye on any goings on in Iraq," a spokesman said.
Reg Keys, founder member of Military Families Against War, whose son Tom died serving as a Royal Military Policeman in Iraq, said while the execution was deserved the price of bringing Saddam to justice had been too high.
"We have lost 127 British soldiers to bring a dictator to book. It wasn't a price worth paying," he said.
"It was never about bringing Saddam to justice in the first place, it was about weapons of mass destruction. Now the goalposts have been moved and it's a different agenda."