Moving away from a free banking era would prove unpopular with consumers, says one expert.
Phil Jones, personal finance campaigner at Which?, believes people already pay for their accounts in some way, although some banks are thinking of moving away from the existing model.
"What our research has shown is that if the banks do want to start levying monthly fees … that would be very unpopular with most consumers," revealed Mr Jones.
The study found that eight out of ten of the 1,022 people polled said they would consider switching to another provider if their bank introduced annual or monthly current account fees.
Seven out of ten believed it would be unfair for banks to charge any additional fees for a current account at the current levels of service they offer, it also found, with many expecting the government to intervene if charges were imposed.
Mr Jones believes there should be some level of choice for people when it comes to deciding on their bank account and advises people to look around for the best deal.