The organisation promoted the idea after a new report found borrowers needing as little as £100 can be charged up to £180 in fees by their bank, if they borrowed the cash across two monthly billing periods.
Daniel Kelly, a credit relations analyst at CAP, told Premier: "We do need some way of saying 'at this point, this level of charges, of cost is just disproportionate', especially when we know that overdraft is something which people really rely on when they're on financial crisis."
A maximum limit on payday lender fees introduced in January 2015 means customers would not have to pay more than £24 in fees.
Daniel Kelly went on to say: "Payday loans can be cheaper than an overdraft in many situations and these charges can really rack up quickly for people who are already struggling.
"When we asked our clients, we found out that almost six in ten were using their overdraft to cover their food, household bills, mortgage or rent, or even paying back other debts."
The consumer group Which?, which produced the report, is calling for action to tackle the "punitive" charges affecting some banking customers.
Vickie Sheriff, director of campaigns and communications, said: "It's not right that people with a financial shortfall can be charged so much more by the big high street banks than they would by a payday loan company, especially if the money is borrowed over two monthly charging periods.
"The Financial Conduct Authority must use its current review to cap these high charges and ensure consumers cannot be charged more for unarranged overdrafts than arranged overdrafts."
Santander and Lloyds said they offer various tools to help customers manage their cash, while NatWest said it encourages customers to contact them if they face going into an unarranged overdraft.
Click here to listen to Daniel Kelly speaking with Premier's Alex Williams: