A video apparently showing the murder of aid worker Margaret Hassan seems to be genuine, says the Foreign Office.
Mrs Hassan made emotional appeals for her life in earlier videos
"We now believe that she has probably been murdered", Foreign Secretary Jack Straw said after analysing the tape.
Her Iraqi husband, Tahseen Ali Hassan, has made a plea for her body to be returned to him "to rest in peace".
Mrs Hassan, who has Irish, British and Iraqi nationality, was seized by an unknown group in the Iraqi capital on 19 October.
British Prime Minister Tony Blair sent his sympathy to Mrs Hassan's family, saying he "shared their abhorrence" at her treatment.
And Bertie Ahern, the Irish Republic's Prime Minister, said her kidnappers "stand condemned by everyone throughout the entire international community".
Arabic TV news channel Al Jazeera has said it has had a copy of the videotape for several days but has chosen not to broadcast it.
The video apparently shows a militant firing a pistol into the head of a blindfolded woman.
A spokesman for Al Jazeera said he presumed the woman was Mrs Hassan.
Mr Hassan has appealed to the kidnappers to return his wife's body.
"I beg those people who took Margaret to tell me what they have done with her," he said.
"They can tell me. They can call the helpline. I need her. I need her back to rest in peace."
Mr Hassan made an emotional plea for her body to be returned
Mrs Hassan's brother and sisters, Michael, Deirdre, Kathryn and Geraldine Fitzsimons, said in a statement that their "hearts are broken".
They said: "We have kept hoping for as long as we could, but we now have to accept that Margaret has probably gone and at last her suffering has ended.
"She had no prejudice against any creed. She dedicated her whole life to working for the poor and vulnerable, helping those who had no-one else."
They described her murder as "unforgivable", adding: "The gap she leaves will never be filled."
Felicity Arbuthnot, a freelance journalist who was a close friend of Mrs Hassan, said she was both sad and angry at the aid worker's apparent death.
"It is an horrific irony that someone who had fought for this country should die in this way," she said.
While the kidnapping was condemned by governments, the aid worker's colleagues and family repeatedly pleaded for her release.
Mrs Hassan, who had lived in Iraq for 30 years, was filmed by her captors asking Tony Blair to pull British troops out of Iraq.
But two weeks ago a message claiming to be from a group led by extreme militant Abu Musab al-Zarqawi called for her release.
Al-Zarqawi's group, which claimed responsibility for murdering Briton Ken Bigley, said her kidnappers did not understand Islam.
"In true Islam, they don't kill women and young children. We only kill those who fight us and kill our people," the message said.
The message was signed "al-Qaeda in Iraq".
Mrs Hassan, 59, was driving to work as director of Care International's Iraq operations when she was seized. The agency has since halted work in the country.
If her death is confirmed, she will be the first foreign female hostage to have been murdered in Iraq amid a recent wave of hostage-takings.