The hostages include a man named as Jason (left) and IT worker Peter Moore
Two bodies feared to be those of British hostages held in Iraq have been handed over, Foreign Secretary David Miliband has said.
Mr Miliband said forensic tests were being carried out on the remains to see if they were of two of the five Britons who were captured in Iraq in May 2007.
The mother of one, who cannot be named for security reasons, said she was "anxious" but "hoping for the best".
There had been speculation earlier this year a deal to free the men was close.
IT consultant Peter Moore, from Lincoln, and four security guards were captured by armed militants at the Ministry of Finance in Baghdad in 2007.
Their captors are a group called the Islamic Shiite Resistance in Iraq.
Security experts understood there had been positive diplomatic moves behind the scenes to free them, including the release of a prisoner whose freedom was being demanded by the hostage-takers.
Foreign Secretary David Miliband: "This is a terrible moment of uncertainty and fear"
Mr Miliband said: "This is a very distressing development.
"We have never speculated on the outcome of this case although we have been working intensively on it, so the overriding feeling today is one of deep sadness and fear."
He said forensic examinations are under way to establish the identities of the bodies and how they died.
"Our immediate thoughts are clearly with the families of the five Britons taken hostage in Baghdad in May 2007," he said.
"As would be the case with any development of this kind, they will fear the worst for their loved ones.
"This is terrible moment of uncertainty and fear for them."
Prime Minister Gordon Brown said he was "saddened and dismayed" by the news.
The mother of one of the guards, who is from South Wales, said: "We are anxious about the situation, yes.
"We have heard nothing new from the Foreign Office, but we are hoping for the best."
Joe Gavaghan, a spokesman for the security company GardaWorld which employed the four guards, said families were not giving up hope.
He said: "The announcement is very concerning. We are certainly not giving up hope that Peter and our four security people are still alive."
BBC security correspondent Frank Gardner
Almost everyone involved in trying to resolve this, Britain's longest-running hostage crisis for a generation, is in shock.
Only a few days ago it was thought that most, if not all, of the five hostages were alive and well and would eventually be released.
In March the kidnappers had released a video of one hostage, Peter Moore, in which he appeared in good health and good spirits.
On 6 June a key Shia militant linked to the kidnappers was released by the US military. It had been hoped this could pave the way for the Britons' release.
Instead, the hostage-takers appear to have responded by delivering bodies.
Mr Miliband called for the immediate safe release of the remaining hostages.
He said he believed those involved in trying to gain the release of the two people whose remains had been handed over had "failed".
"I think British people understand why no British government makes concessions in return for hostage-taking," he added.
"Hostage-taking is never justified in any cause.
"Today's terrible news underlines the gravity of the crimes associated with it," Mr Miliband said.
He also praised the help the Iraqi authorities had given in attempts to free the Britons.
"I urge those working for peace and progress in Iraq to redouble their efforts to secure the release of all the hostages held there."
Little is known about the identities of the men because of a media blackout during a large period of their captivity.
The blackout originally came came on the instruction of the hostage-takers who said they did not want publicity.
The militants have released videos of the captives, including one - broadcast on Dubai-based TV station Al-Arabiya - warning that a hostage would be killed unless British troops withdrew from Iraq.
Mr Moore had been working for American management consultancy Bearingpoint when he was kidnapped, while the other men were contractors employed to guard him.
The names of the four security guards are understood to be Jason, Alan, Jason and Alec.
Little else is known about them, other than that the guard Alan is from Dumbarton in Scotland and at least one other is from South Wales.