Cooper, who is professor of organisational psychology and health at Lancaster University Business School, resigned from his role at the charity yesterday, after its founder, Christine Pratt, told the Today programme on Radio Four two of the calls to the helpline had come from the deputy prime minister's office but neither had accused the prime minister himself of bullying.
Pratt was responding to comments from business minister Peter Mandelson that there was no culture of bullying at Downing Street.
But speaking this morning to HR magazine, Cooper said: "I don't care what Peter Mandelson said; Christine Pratt did not have all the facts and breached confidentiality by talking to the press.
"This is not a political issues. Managers are more likely to be abrasive during a recession and that leads to a higher likelihood of staff feeling bullied. But what the helpline should have done was to tell staff to go to their HR department.
"If an employer is named, then the employees who called the helpline could potentially be found out. This would put off other employees from calling."
Cooper did not comment on whether he believes Pratt should resign over the issue. He added: "It is not my judgment call as to whether or not Pratt should resign. I was patron of the organisation, but I am not a trustee. That decision lies with them.
"But this should not be the start of an anti-bullying campaign and the organisation must set guidelines to ensure this does not happen again. If this came from a leak, it would be different but Pratt approached the press and that should not have happened."
