A Labour government would cap the credit card bills of more than three million customers, a move that would cost banks and other card providers at least £13 billion.

John McDonnell, the shadow chancellor, will promise today that no card holder would be forced to repay in interest payments more than the sum they initially borrowed.

The Financial Conduct Authority estimates that three million credit card holders are in “persistent debt”, defined as owing at least twice the original sum borrowed after 18 months.

The watchdog wants lenders to do more to help, identifying those likely to be trapped in debt if they make only the minimum repayment on their cards for a year and a half and taking action if customers haven’t cleared their balances in another 18 months.

That could include forgiving some of the debt and forcing borrowers to take better-value personal loans to clear the remainder. Under proposals to be unveiled this autumn, lenders could also face restrictions on offering to increase credit limits for those who are failing to keep on top of their credit card debt.

The watchdog estimates that banks could lose about £13 billion over the next 12 years in lost interest payments as a result. The average amount owed by those in persistent debt, about one in ten customers, is £3,464.

Labour’s plans go much further, to make banks legally unable to charge interest on sums that amount to twice the original sum. “We have seen with payday loans that some companies were making massive profits from people’s financial difficulties,” Mr McDonnell will say today in his speech to Labour Party conference.

“The government has been forced to cap interest payments on payday loans. But more than three million credit card holders are trapped by their debt. They’ve paid more in interest charges and fees than their original borrowing.

“The Financial Conduct Authority has argued for action to be taken on credit card debt as on payday loans.

“I am calling upon the government to act now to apply the same rules on payday loans to credit card debt.

“It means that no one will ever pay more in interest than their original loan. If the Tories refuse to act, I can announce today that the next Labour government will amend the law.”

Details of the policy that have not been explained include what incentives borrowers would have to repay a capped loan or what would prevent them running up debts on another card. Providers are also likely to protest that the policy would drive up the costs for all holders as well as restricting access to convenient credit. Labour will brush off warnings of unintended consequences as it seeks policies that resonate with voters at a time of increasing household debt and stagnating living standards.

A spokesman said that credit card debt was becoming a “growing problem and threat to our economy”.

Mr McDonnell will say: “Household debt in this country stands at the record level of over £1.8 trillion.”