The sale was demanded by European regulators after Lloyds bought HBOS during the financial crisis and will affect the TSB and Cheltenham & Gloucester brands.

Upon completion, the Co-operative Group will have around 1,000 branches and 4.8m customers.

It will pay an initial consideration of £350m, and up to an additional £400m in present value, equivalent to around £800 million on a nominal basis, based on the performance of the Co-operative’s combined banking business from completion up to 2027.

The completion of the transaction is expected by the end of November 2013, although it will be subject to regulatory approvals from the FSA, HM Treasury and the European Commission.

António Horta-Osório, group chief executive, said: “Today’s agreement is an important step in meeting our obligations under the mandated sale of our branches.

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“We believe the Co-operative will be a good owner for our business, customers and colleagues, and the combined banking business will be a significant competitor on the high street with nearly 10 per cent of today’s UK branch network.”

Adrian Coles, director general of the BSA, said: “We welcome today’s announcement which takes us several steps closer to a significant expansion in the mutual sector. Mutuals are increasingly providing an alternative for consumers looking for value for money, good customer service and a different approach to financial services.”