Friends of Norman Kember say they are relieved a new tape of the Iraq hostage has emerged, but fear his kidnappers could be "at the end of their tether".
Norman Kember in the latest video
Mr Kember, 74, of north London, was seized in Baghdad with two Canadians and an American on 26 November.
The video - the first news of the men for seven weeks - says they will be killed if the kidnappers' demand that Iraqi prisoners are freed is not met.
The Foreign Office is assessing the tape, which was aired by al-Jazeera TV.
A Foreign Office spokesman said: "It is a relief to see Norman Kember and his friends and colleagues still alive after so long without word, and we are urgently assessing the video. We continue to do all we can."
TIMELINE OF ABDUCTION
26 November: Norman Kember abducted along with three other peace workers
30 November: Video footage of the hostages aired on al-Jazeera
2 December: Second video of the hostages aired. Their captors threaten to kill them unless their demands are met by 8 December
8 December: Third video is aired on al-Jazeera showing Mr Kember and US hostage Tom Fox wearing orange jumpsuits, blindfolded and shackled. The captors' deadline is extended to 10 December
28 January: New video of hostages, dated 21 January, aired on al-Jazeera
Mr Kember's fellow captives are Canadians James Loney, 41, and Harmeet Singh Sooden, 32, and American Tom Fox, 54.
The group were travelling with Canadian-based international peace group Christian Peacemaker Teams when they were seized by a group calling itself the Swords of Truth.
Al-Jazeera said it had aired the whole of the latest recording of the men, which was about 55 seconds long, but the Qatar-based TV station would not say how it had obtained the tape.
In the video, which is dated 21 January and shows the four hostages standing against a wall, the men appear to be speaking but their words are not audible.
Instead it includes a message from the kidnappers repeating their demand that all Iraqi prisoners be freed.
The kidnappers had originally set a deadline of 8 December for this demand to be met. This was later extended by two days to 10 December and there had been no news of the hostages since.
Rebecca Johnson, spokeswoman for Christian Peacemaker Teams in Canada, said it was relieved to see the men alive on the tape.
"This news is an answer to our prayers. We continue to hope and pray for their release," she said.
Anas Altikriti, of the Muslim Association of Britain, who has been campaigning in the Middle East for Mr Kember's release, said the video showed there had been "some kind of breakthrough" in the efforts to communicate with the captors.
He said he still did not know who was holding the men or where they were, but the video was a positive sign that they were still being held by the same group.
However, he added: "There are some positives out of all this, but we have to work very fast now. No deadline may mean they could be at the end of their tether."
The Reverend Alan Betteridge, a friend of Mr Kember for more than 40 years, said he was concerned the kidnappers were still making the same demands "couched in these threatening terms".
However, he said Mr Kember's wife, Pat, was "coping very bravely and strongly".
BBC correspondent Nicholas Witchell, in Baghdad, said the group was making political demands which could not be met.
He said the US had released 420 prisoners, including five women, two days ago but there were many thousands of people still in detention.