Peter Moore was working as a computer consultant in Iraq
He said the taking of hostages would not change British policy in Iraq, and the government would do everything in its power to secure their release.
One of the hostages has now been identified as Peter Moore, who was working as a computer consultant.
Mr Moore has previously worked for the VSO voluntary group in Guyana.
A video tape made by the kidnappers was broadcast on Tuesday.
'Bravery and resilience'
The prime minister said his first thoughts were with the five hostages, who were kidnapped iin Baghdad in May, and their families.
He said they had endured "an enormous" amount over the last six months and he wanted to thank them for their "bravery and resilience".
The taking of hostages is completely unjustified, wholly unacceptable
Prime Minister Gordon Brown
He said: "We will do everything in our power to secure our objective, which is the immediate release of the hostages."
Mr Brown paid tribute to the Iraqi government for its efforts to try to secure the hostages' freedom and added: "We will give them our full support."
The five men - four guards and a computer expert - were seized in May from Baghdad's finance ministry building by gunmen disguised as police officers.
A militia group calling itself the Islamic Shia Resistance in Iraq is now holding them captive.
The video tape of the men, dated 18 November, contains a threat that one of them will be killed unless UK forces are withdrawn from Iraq.
'Completely unacceptable'
The message issued by their families encourages the men to stay strong and positive in the face of adversity.
It states: "You are constantly in our thoughts. While the pain of missing you does not go away we are all staying positive for you and hope that you are looking after yourselves and keeping your spirits up as much as you can under such circumstances."
The prime minister said: "The taking of hostages is completely unjustified, wholly unacceptable and we are making it clear they will not change our policy in any way.
"I want the hostage takers to accept their responsibility, to understand the consequences of what they are doing, to make possible the immediate release of the hostages, to allow them to come home at the earliest opportunity.
"We will do everything in our power. The taking of hostages is completely unacceptable. We are demanding the immediate release."
The case has not featured in the media as much as other kidnappings in Iraq - including those of Ken Bigley and Margaret Hassan - because of a Foreign Office request for minimal coverage.
The Foreign Secretary, David Miliband, told Sky News it was a "very dangerous situation" and it would be wrong for him to get into a "running commentary" on what the government was doing.
He said: "It's important that publicity is never confused with activity. And especially in a case like this, its very, very important that we follow a very careful strategy.
"The distress of the families is going to be huge. It's bad enough to have the hostage taking.
"To then have the video coming out last week is just going to add hugely, has added hugely to the distress.
"But the whole of the British government is working very, very actively on this. The prime minister's statement refers to this."
British Prime Minister Gordon Brown has called for the immediate release of 5 British hostages abducted in Baghdad, Iraq last May. 

For the first time since the 5 Britons were abducted on May 29 from a Finance Ministry compound by gunmen posing as police officers, a video released Tuesday by a group called the Islamic Shia Resistance in Iraq showed one of the men being held. It was the first public evidence that the men might still be alive.

"My name is Jason and today is the 18th of November," said one of the hostages.

In that video, the captors say they will start to kill the hostages, who include four security guards and one computer expert, if Britain does not withdraw all of its remaining troops from Iraq soon.

Over the months, little if anything has been disclosed about what Britain is doing to gain the release of those held. Today,  Brown underlined that behind the scenes, things were being done.

"The taking of hostages is completely unjustified, wholly unacceptable and we are making it clear they will not change our policy in any way," Brown said. "We will do everything in our power to secure our objective, which is the immediate release of the hostages." He however stressed that Britain will not be making any kind of deal to gain the release of the five.

Speaking on Sky News, British Foreign Secretary David Miliband spoke of the stress the families of those being held are under.

"It is important that publicity is never confused with activity, and especially in a case like this, it is very, very important that we follow a very careful strategy," said Miliband. "The stress of the families is going to be huge. It is bad enough to have the hostage-taking. To then have the video coming out last week is just going to add, has added, hugely to the distress. But the whole of the British government is working very, very actively on this."

The family and friends of the hostages also appealed for the release, in an emotional appeal which took place on Wednesday.
Brown also praised Iraqi Prime Minister Maliki and his government for their efforts to free the men.