However, 51% of the 2,083 adults surveyed by YouGov in March said they do not want to pay for privacy when using online services.
The YouGov study also found that 72% of consumers in the UK are "concerned about their private information online". The research was commissioned by information security provider CloudMask.
According to the study, 29% of consumers believe they are mostly responsible for their online privacy, but the UK's data protection watchdog said it does not absolve businesses of their responsibilities under the Data Protection Act.
"Consumers are becoming much more aware of the need to protect their personal data online and even though this survey shows they might be prepared to pay to do that, it is still ultimately the responsibility of the businesses who hold that data to make sure they follow the laws around data protection," Garreth Cameron, group manager for business and industry for the Information Commissioner's Office, said.
"Businesses should be doing everything they can to keep information safe by investing in consumer privacy online, both in terms of education, increased protection and good practice," he said.