Mr Cook said that he had received a "very positive response" from Mr al-Iryani.
British Consul-General David Pearce saw three of the men late on Friday. Although relatives have claimed that two of the detainees had been shot at while in jail, Mr Pearce said that he had not found proof of this and that the men he visited looked "reasonably well". He was unable to see the other two because of "bureaucratic problems"- one detainee has joint British and Yemeni nationality while the other has a problem with his passport.
The five are accused of belonging to a Western sabotage group which is linked to an alleged militant Islamic group that kidnapped 16 Western tourists on 28 December. Three British tourists and one Australian were killed a day later in a controversial rescue attempt by the Yemeni army.
The men were arrested in Aden on Christmas Eve. The Interior Minister Hussein Mohammad Arab announced last week that eight people had been arrested, but a Foreign Office spokeswoman said yesterday that only six arrests had been made - the other detainee is a French national.
The six are also being questioned about alleged plots to bomb targets in Yemen, including the British consulate.
Relatives said that they were told that the group would be tried yesterday, but Mr Pearce said that a trial is not imminent, as the Muslim holy month of Ramadan does not end until 18 January.
If convicted, the men could face the death penalty. Amnesty International has expressed concern that the men could be mistreated because of the nature of their alleged crimes.
Late last year, the Yemeni army newspaper claimed that Britain was harbouring militants who were involved in a number of bombings in which several people were wounded or killed. It said that the terrorists had staged their attack from London.
Hundreds of supporters staged a demonstration yesterday outside the Yemeni embassy in London, calling for the Britons to be freed.
The detainees' families said that they had visited Yemen to learn Arabic, study Islam and see their relatives, a normal practice in the month of Ramadan.