The survey, which took in more than Facebook 1500 users, found that, whilst almost two-thirds of Facebook members are considering leaving, 16% of those polled claimed to have already stopped using Facebook as a result of inadequate control over their data.
Just 12% said they would not quit Facebook, and the same percentage again said they did not think it likely they would leave.
As previously reported by Infosecurity, Facebook has faced growing criticism over changes to the way that the social network can share user data across its site and with other websites.
Concerns have focused on the complexity and opt-out approach to sharing member information with wider networks. Media reports suggest that Facebook is planning to announce changes to its privacy settings within the next few days, but it is unclear as to whether any changes will be substantial enough to address user's concerns.
"This poll shows that the majority of users are fed up with the lack of control that Facebook gives users over their data", said Graham Cluley, Sophos' senior technology consultant.
"Most still don't know how to set their Facebook privacy options safely, finding the whole system confusing. What's needed is a fundamental shift towards asking users to opt-in to sharing information, rather than to opt-out", he added.
Noting that a mass exodus from Facebook is unlikely, Cluley said in his security blog that users are clearly getting more interested in knowing who can look at their data. As a result, he adds that Facebook needs to ensure that further changes to its privacy policy are clear and concise.