The UK government is coming under increasing pressure to secure the freedom of three Britons abducted in Iraq in May 2007.
It follows the release of the bodies of two British security guards, kidnapped along with the missing three men.
Gordon Brown called for the remaining hostages to be freed, but opinion is split over the UK's negotiation policy.
There have been accusations that the UK's approach of not negotiating with hostage-takers endangers lives.
Former Liberal Democrat leader Sir Menzies Campbell said negotiations with those holding the remaining three hostages should now be stepped up.
So far, the government has said it is sticking to its line of not making "substantive concessions" to kidnappers.
On Sunday the Foreign Office (FCO) said the two bodies, handed over to UK officials in Iraq, were "highly likely" to be those of Jason Swindlehurst, from Skelmersdale, Lancashire, and Jason Creswell, from Glasgow.
The FCO said it had "grave concerns" about the safety of the remaining hostages - IT consultant, Peter Moore, and two bodyguards, who have been named only as Alan, from Dumbartion, and Alex, from South Wales.
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The prime minister said: "There is no justification for hostage-taking and I call on those people who are holding the other Iraqi and British hostages to release them immediately."
The British government's policy of not making substantive concessions has been criticised by some and praised by others, including some North African countries who have attacked other European nations for paying huge ransoms to kidnappers..
But Sir Menzies said he would encourage the UK government to re-open contact with the hostage-takers.
"I'd be getting onto every conceivable contact that there might with those who are holding them," he said.
"I would be saying through those intermediaries - you have deeply, deeply, disturbed and upset and, in fact, even angered us, in relation to these two men whose remains have now been produced.
"But there is still the possibility that we can reach an accommodation which brings about the release of the other three. I would not, as it were, give up hope .''
Former hostage Terry Waite, who was held in Lebanon for more than four years, said the UK's approach to the situation was correct.
"This actual policy of not doing deals, not getting into that sort of business with hostages, is in the long run a right policy, because if you do other sorts of deals, you simply encourage further hostage taking," he said.
Freelance journalist James Brandon, who was held for 24 hours by militants in Basra in 2004, suggested Britain may need to alter its policy of never negotiating with hostage takers.
He said: "This has been the British government's policy for a long time, that you're not going to negotiate with these people, you're not going to give in to their concessions, but at the same time this seems to be a strategy that isn't working at the moment.
"We've had British hostages kidnapped and killed in Iraq, in west Africa most recently. The present strategy isn't delivering results, it seems to be making life more dangerous for people, rather than safer."
Former Foreign Office Minister, Kim Howells, who was involved in trying to negotiate the hostages' release when they were first taken, said the government had done all it could to free them.
He told the BBC: "In the best part of four years that I was in the Foreign Office, I don't know of another operation that was better resourced, that more energy was put into.
"Every stop was pulled out to try and find these men."
'Deeply shocked'
Mr Moore, from Lincoln, and his guards were captured by armed militants at the Ministry of Finance in Baghdad in May 2007.
It is thought the handover of the bodies may have been prompted by the release of Shi'ite militant Laith al-Khazali, on 6 June.
BBC security correspondent Frank Gardner said Mr al-Khazali's freedom had been a stipulation for the hostages's release.
He added the kidnappers were likely to be a rebel offshoot of the more mainstream Mehdi Army - and were thus proving difficult for even Iraqi mediators to deal with.
The aim of the kidnappers - who call themselves the Islamic Shiite Resistance in Iraq - is to obtain the release of their comrades from Camp Cropper, a US military prison west of Baghdad.
The security firm, Gardaworld, which employed the dead men paid tribute to their bravery and said they were "deeply shocked" by the news.
A spokesman said: "These two professionals were outstanding individuals and experts who commanded the respect of all those who knew and worked with them."
The daughter of one of the dead men, Jason Creswell, wrote him a letter when her family still thought he was alive.
Seven-year-old Maddi Creswell said she missed her father and wanted him to come home.
Mr Moore's father Graeme, from Leicestershire, said waiting for news that he was not one of the dead men had been "torture".
