The government says it respects the decision made by its Iraqi counterpart to execute former president Saddam Hussein.
But foreign secretary Margaret Beckett has reiterated Britain's opposition to the death penalty.
Saddam was executed this morning at 06:00 local time (03:00 GMT) in Baghdad, 27 years after he first came to power.
The former dictator, ousted from power by US-led coalition forces in 2003, was found guilty last month of crimes against humanity over the massacre of 148 Shia Muslim men in the village of Dujail in 1982.
On Boxing Day, an Iraqi appeals court upheld the guilty verdict and death sentence. Under the country's law Saddam had to be executed within 30 days of the appeal's rejection.
The death warrant ordering the execution was signed by vice presidents Tariq Hashimi and Adel Abdul Mehdi. President Jalal Talabani did not sign the warrant, choosing instead to transfer his authority to prime minister Nouri al-Maliki.
"Criminal Saddam was hanged to death," announced a state-run television station.
And Ms Beckett today said Saddam had been "held to account".
"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," she said.
"We have made our position very clear to the Iraqi authorities, but we respect their decision as that of a sovereign nation."
The foreign secretary continued: "Iraq continues to face huge challenges. But now it has a democratically-elected government which represents all communities and is committed to fostering reconciliation.
"We will continue to work with this government and with the Iraqi people to build security and prosperity for the future."
US president George Bush said that a "difficult year" for the US army had been brought to an end, but claimed that Saddam's death would not signal a close to the sectarian violence that has blighted the country since the dictator was toppled.