A Foreign Office spokesman said the footage was a longer version of the video aired on Aljazeera on Friday and had been available on websites for a number of days.
The footage, which was broadcast on British television on Wednesday, shows Kember in handcuffs and shackles calling on Blair to withdraw troops from the war-torn country.
Kember, a grandfather from northwest London who is a lifelong peace campaigner and human rights advocate, is heard saying: "I ask Mr Blair to take British troops out of Iraq and leave the Iraqi people to come to their own decisions on their government."
Kember, 74, and his three colleagues from Christian Peacemaker Teams (CPT) - American Tom Fox, 54, and Canadians James Loney, 41, and Harmeet Singh Sooden, 32 - were kidnapped in Baghdad on 26 November.
The previously unknown Swords of Righteousness Brigade has threatened to kill them unless all detainees in US and Iraqi prisons are released by Thursday.
Working for oppressed
CPT, a non-government organisation campaigning for peace, called on Tuesday for their release.
"We appeal to your humanity to show mercy on our brothers and let them come back safely to us to continue our work," said CPT, which has offices in Canada and the US.
Tom Fox's (C) daughter says her
father rejects a violent rescue
"As you can see by the statements of support from our friends in Iraq and all over the world, we work for those who are oppressed," it said in a statement to the kidnappers.
"We also condemn our own governments for their actions in Iraq," said CPT, one of the few remaining aid groups operating in Iraq.
Also on Tuesday, the daughter of the American hostage appealed for his life, telling his captors that killing him would not advance their cause.
Katherine Fox, Tom Fox's daughter, said in an interview with ABC's Nightline programme that her father was in Iraq working on behalf of Iraqi detainees and their families.
She said she wanted to remind her father's captors that he opposed the US occupation of Iraq and had campaigned against it.
"And that the work that he is there to do is the same work that they would like to see done. And that I do not think a loss of his life benefits their cause," Fox said.
"There is a need to help the Iraqi people, especially at a time when so many organisations are no longer able to be present because of the danger"
Katherine Fox, daughter of kidnapped aid worker Tom Fox
Fox rejected the view of conservative radio talk show personality Rush Limbaugh that for her father to be in Iraq without protection was essentially asking for trouble.
"I don't think that he even saw it as asking for trouble. He saw a need," she said. "There is a need to help the Iraqi people, especially at a time when so many organisations are no longer able to be present because of the danger."
Fox deplored the kidnapping, but said she knew that her father did not support violence as a way of resolving the hostages' situation.
"Before he left, he wrote a very concise, precise statement of conscience and conviction that if he were ever to be taken hostage that he does not support violent means to come in and to potentially release, to rescue him," she said.
Contact with kidnappers
The group that claimed responsibility for kidnapping them posted a video last month of the four men and accused them of being "spies working for the occupying forces" under the guise of a Christian group.
British Foreign Secretary Jack Straw on Monday said the government was ready to hear from the kidnappers, but was unable to confirm reports that direct contact had been made with them.
A Western diplomat told the BBC that such contact with the hostage-takers had been made.
A Frenchman and a German woman were also kidnapped in Iraq in the past week.