Britain said Uday and Qusay Hussein made what proved to be a fatal mistake when they rejected offers to go into exile earlier this year.
The British foreign secretary, Jack Straw, said the deaths of the Hussein brothers followed months of enticements for them and their father to leave Iraq.
Mr. Straw summed up his reaction to the deaths in an interview on British radio. "I'm not rejoicing. I mourn the death of anybody. But it has to be said that it is a very great relief for all Iraqis. And I may say that Uday and Qusay, along with their father, were given opportunities to remain alive that they never gave a lot of their victims," he said.
The foreign secretary recalled that in January, he and U.S. Defense Secretary Donald Rumsfeld had offered the Husseins exile outside of Iraq.
Mr. Straw said that in March, the United States and Britain gave Saddam Hussein and his entourage what he called a "clear ultimatum to leave the country" shortly before the start of the U.S.-led invasion.
Mr. Straw described the Hussein brothers as "extremely unpleasant psychopaths" who supervised what he called "a reign of terror" against Iraqi citizens.
In another Iraq-related development, the British Broadcasting Corporation has announced that it has a recording that could back up a disputed news report that said the government exaggerated the military threat from Iraq before the war.
The BBC said the recording is of a conversation between television journalist Susan Watts and David Kelly, a British weapons expert who apparently committed suicide last week.
The BBC said that on the recording Mr. Kelly expresses doubts about the way intelligence on Iraq's weapons threat was presented by the government. The broadcaster said the recording will be presented to an inquiry investigating Mr. Kelly's death.
In a news report broadcast in May, the BBC quoted intelligence sources as saying the government had overstated Iraq's military capabilities by claiming Iraq could launch weapons of mass destruction within 45 minutes.
The government has repeatedly denied the charge, which has spawned a parliamentary inquiry.