LORD McConnell has spoken of difficult times he and his family have endured since learning that they had become potential victims of phone hacking.
The former First Minister confirmed he is taking legal action against Rupert Murdoch's News International.
The Labour peer was informed by Scotland Yard that his name and those of his son Mark and daughter Hannah, with their phone numbers, had been found in the notes of private detective Glenn Mulcaire, who worked for the News of the World.
A friend of the McConnells said since they had been contacted by Strathclyde Police officers on behalf of the Metropolitan Police in February, there has been regular contact as detectives try to piece together how often and to what extent their phones were hacked.
It is thought any hacking took place during the time Lord McConnell was First Minister from 2001 to 2007 when his son was at university and his daughter had started a new job.
"They had suspicions as a family their phones were hacked and are now hopeful the police will get to the bottom of their suspicions," said the friend.
"Jack was always very careful never to use his son or daughter for political purposes and it is absolutely sickening their private lives might have been eavesdropped," he added.
The peer was reticent to talk about the issue as police are still investigating. He said: "This is a difficult situation. I don't want to discuss details but I can confirm we have spoken to the police and are taking legal action."
In January, actor Jude Law and the former Deputy Prime Minister Lord Prescott were among the hacking victims, given payouts of £130,000 and £40,000 respectively. Sara Payne, the mother of murdered schoolgirl Sarah, was given an undisclosed sum.
Five years ago, Mulcaire and former News of the World royal reporter Clive Goodman were jailed after they admitted intercepting voicemail messages left on the phones of royal aides.
At Westminster, where the Commons Culture Committee will publish its findings on the phone-hacking scandal tomorrow, Shadow Scottish Secretary, Margaret Curran said the news that Lord McConnell and his family were potential victims was "very distressing" but accused Alex Salmond of a cover-up in his own "murky deals with the Murdochs".
She said: "People will be horrified to hear of this intrusion into the lives of Jack and his family."
Ms Curran argued that the revelation intensified the pressure on the First Minister and that he needed to make clear whether he knew of the police findings. "It is unbelievable that after one first minister was hacked by Rupert Murdoch, his successor is still defending him.
"Even after the sick revelations this summer about hacking the phone of a missing teenager, he became the only leader in Western Europe to invite Rupert Murdoch round for tea.
"The development makes Mr Salmond's decision to act as an undercover lobbyist for the Murdochs look increasingly unwise," insisted Ms Curran.
She said she was shocked to see how differently Holyrood and Westminster had responded.
"The Scottish Government's response to this growing scandal is weak and insufficient."
A spokesman for Alex Salmond said: "It is disgraceful that Mr McConnell and his family could have been subjected to such intrusion. The First Minister condemns outright all examples of phone hacking and other press malpractice regardless of who the victims are and who the perpetrators were.
"In addition he has every confidence that Strathclyde police will vigorously pursue, without fear or favour, any evidence of criminality committed against any Scottish citizen."
News International declined to comment.
Andrew McKie: Page 13
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