A further 21 percent indicated that they would feel 'annoyed' by such a ban.
The problem is less acute with 25 to 65 year-olds, of whom just 16 percent would consider leaving and 13 percent would be annoyed.
Mark Hutchinson, managing director of Telindus, said: "An outright ban on personal internet usage is clearly not the right approach.
"However, the challenge is to achieve the right balance between allowing employees personal internet time without jeopardising the bandwidth required for business applications.
"It is commercially unwise to have a bandwidth free-for-all, especially when you consider that downloading a single half-hour TV show consumes more bandwidth than receiving 200 emails a day for a year."
Companies are increasingly looking to ban sites like Facebook because they clog up corporate networks and take up employees' time.
Interestingly, the survey revealed that employees would be supportive of a ban if it made other network functions faster.