The Government will give a new regulator the explicit power to cap the interest rates charged by payday lenders, Treasury minister Lord Sassoon has announced.

Lord Sassoon's concession came in the face of an amendment put forward by Labour and backed by the incoming Archbishop of Canterbury.

The minister told peers: "We need to ensure that the Financial Conduct Authority grasps the nettle when it comes to payday lending and has specific powers to impose a cap on the cost of credit and ensure that the loan cannot be rolled over indefinitely should it decide, having considered the evidence, that this is the right solution."

His announcement came at report stage of the Financial Services Bill after shadow business minister Lord Mitchell said some payday lenders were charging annual interest rates of 4,000% on short-term loans.

The Bishop of Durham, the Rt Rev Justin Welby, who will take over as Archbishop of Canterbury next year, said the rates being charged were "clearly usurious".

Lord Sassoon said if Lord Mitchell withdrew his amendment, he would bring forward a Government change to the legislation when the Bill has its third reading next week. He said the Government had always been clear that the FCA "should be able to take action to address the problems that are rife in the payday loans sector".

The Treasury insisted the Bill as currently drafted would give the FCA the power to cap rates, but Lord Sassoon said he wanted to embed "stronger payday loan regulation in primary legislation".

Lord Sassoon said the Government could go further than Lord Mitchell's amendment and also "put in place stronger automatic consumer protections and make the deterrent more robust by providing that a breach of these rules would make the agreement unenforceable by the lender".

On the Government's proposed amendment, he said: "I can confirm, explicitly, that it will cover both the total cost of credit and the total duration of credit."

Lord Sassoon said the FCA would have to study the evidence before deciding whether to impose a credit limit. Capping the cost of credit and the number of times the loan can be rolled over was a "major market intervention" which could benefit customers, as a study in Japan had indicated. But he added: "Experience in Germany and France has shown there can be equally momentous unintended consequences including reduced access to credit for the poorest and most vulnerable consumers, even driving them to illegal loan sharks."

The Press Association, photo by HowardLake