A spokesman for the families, Rashad Yaqoob, told a press conference he had received the information from an unidentified source in Yemen.
The Foreign Office was last night unable to confirm the reports, as the British consul in Yemen has been allowed only a brief visit to four of the men. The fifth is a dual citizen and considered a Yemeni national by the authorities.
The lawyer representing the men in Yemen has not been able to meet his clients despite having a written order allowing him to do so.
The developments come amid mounting speculation that the three Yemeni gunmen arrested for the kidnap of 16 Western tourists last month are due to stand trial within the next 48 hours.
Mr Yaqoob denied the five Britons - Shahid Butt, 33, Malik Nasser Harhra, 26, Samad Ahmed, 21, all from Birmingham, Ghulam Hussein, 25, from Luton, and Mohsin Ghalain, 18, from London -.were linked to a bomb plot. But he did confirm that Mr Ghalain was the stepson of Abu Hamza, an imam based in London who openly promotes the overthrow of the Yemeni state.
The fury of the families contrasted sharply with the experience of Katherine Brooke, wife of John Brooke, kidnapped by Yemeni tribesmen last week.
"I am overwhelmed by all the encouraging messages I have received from the public and for the tremendous help of the Foreign Office and the support of the local police," she said yesterday.
Mr Brooke has told his company by telephone that he is being well treated by the tribesmen.
The families of the five Britons in custody said the Foreign Secretary, Robin Cook, had failed to contact them since their relatives' arrest before Christmas.
Questions about possible links with Sheikh Hamza and his group, the Supporters of Shariah, brought angry shouts from the floor, but Monica Davis, wife of Ghulam Hussein, said she had very little knowledge of the cleric.
"I don't know much about him or his group, but I have done my own research and if there were any links with him and terrorism he would have been shut down by the CIA or MI5," she said.
The families warned there would be blood on the streets if any of the men were executed by the Yemenis.
The Yemeni lawyer acting for the men, Badr Basunaid, said yesterday the police were still refusing him access to his clients, despite obtaining written permission from the Chief Prosecutor of Aden.
"I have no access, it is impossible for me to do my job properly," he said. "There is no reason why I should not have access, but it means that things are now going very slowly."
Yesterday Foreign Office sources said they were investigating reports that the trial might start within 48 hours of three men arrested by security forces after a shoot-out with kidnappers. The hostage-taking led to the murder of three British tourists.
While there are other reports that the trial will not begin until the end of Ramadan - likely to be 18 or 19 January - the British ambassador in Yemen, Vic Henderson, dispatched his vice-consul from the capital, Sanaa, to Aden yesterday to investigate the claims.
Mr Basunaid expressed concern over the possibility of such a trial, saying that those defendants might have been forced to make claims against his own clients.