Staff at the Winchester offices can use the site during breaks
Hampshire County Council is threatening to block staff from using the social networking site Facebook.
Bosses said they noticed an increase in use and during monitoring 46 employees were found to have regularly spent more than an hour on the site each day.
The campaign group Taxpayers' Alliance said the workers were "wasting" taxpayers money.
The county council said it would block the site to any employee using it in an "unacceptable" way.
Leader of the council Ken Thornber said employees at the Winchester base were allowed to view the sites at work during breaks.
Susie Squire, from the Taxpayers' Alliance, said: "Ultimately these people work for taxpayers in Hampshire.
"There is no way they should be spending this time when they are supposed to be doing their jobs on a social networking site."
Other social networking sites and dating websites could also been blocked to staff.
Cllr Thornber added: "We have seen an increasing trend of the use of social networks.
"We are monitoring it carefully and if we feel there is any abuse we will block the use of that individual and they could be disciplined.
"We review these things and that's how we know that it is being kept within reasonable limits.
"But if not we will stop it."