Returning to the state-owned al-Rashid hotel after the six-hour visit to Abu Ghraib prison, the relatives looked cheerful and spoke to the press for the first time since leaving London on Sunday.
'They are very well looked after,' said Julie Ride, referring to her husband, Paul, and his fellow-prisoner, Michael Wainwright. Holding her 18-month-old son, William, Mrs Ride said that the visit went 'very well'.
Asked if the mission would result in freedom for the two men, Mrs Ride said: 'We don't . . . We can't say that. We don't know.'
Mr Wainwright, 42, and Mr Ride, 33, are serving sentences for illegally entering Iraq.
Iraqi officials had no immediate reaction to the visit. Baghdad has linked an early release to demands that the British government free Iraqi assets frozen during the Gulf war.
'We are asking the Iraqi government what their intentions are in relation to these two men,' said the director-general of the British Red Cross, Michael Whitlam, who accompanied the relatives from London.
With the Ride family are Mr Wainwright's mother, Iris, and his sister, Heather Horne. William Ride lay sleeping and sucking on a dummy as a Russian embassy car drove them into the prison. Mr Ride awakened the child, Mr Whitlam told reporters later, and the families embraced and wept tears of joy.
Mr Whitlam said the men 'are looking fit and well', adding: 'It is a very personal meeting. The prison authorities said they can stay as long as they like.'
Mr Whitlam refused to answer questions on the status of the prisoners, saying he was awaiting further meetings with Iraqi officials. He had nothing to report from a morning meeting with authorities, but said he remained 'optimistic' for a release. 'I haven't had a chance to speak to anyone high enough yet to give me a response,' Mr Whitlam said.
Iraq's state-controlled media did not report the activities of the British families. Ties between Britain and Iraq have been broken since the Gulf war. The visit comes as Baghdad shifts away from the confrontation that led to bombing raids by US, British and French planes last month.
Mr Ride, a chef working in Kuwait, was sentenced to seven years imprisonment after his arrest at the disputed border with Iraq in August. Mr Wainwright is serving 10 years. He was arrested in May after crossing from Turkey into the Kurdish-controlled area of northern Iraq. He said that Iraqi guards had let him in.