"People are so frightened they will not put their heads above the parapet," said Johanna Baxter, national officer for PCS, the trade union which represents people working in or for government agencies.
Earlier this month FE Focus revealed that a leaked consultants' report showed there was a "culture of fear" at the LSC, with people afraid of being slapped down in front of colleagues if they dared to speak their minds.
The report was commissioned to discover if the council was ready for Investors in People status.
"I have made complaints to the LSC, and to the national office, including even the way I have been treated. This is very, very serious," said Ms Baxter.
The national LSC would not be drawn on the numbers of people making formal complaints. A spokeswoman said a process existed which was there to protect employees.
"The LSC does not want people to work in a place where they are bullied or harassed. There are processes in place to deal with this."