The customers will be changed to the new TSB name from next year, which will eventually be dropped for the Co-op name, unless these customers opt to stay with Lloyds.

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.”

“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.”

This 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 from the deal.

It will pay an initial consideration of £350m, and up to an additional £400m in present value, 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.

Kevin Mountford, head of banking at MoneySupermarket said: ” The deal will more than double The Co-operative Bank’s branch network to almost 1,000 and will give it an additional five millions customers, taking its market share from 1% to 7% overnight.”

“As we have seen over recent weeks following the recent banking turmoil, many smaller banks, including The Co-operative Bank, have benefited from customers switching away from the big banks.”

“Creating a new ‘real’ challenger to the big banks may be the antidote the sector needs, and may encourage a culture of switching which has been lacking over the past few years, especially as The Co-operative Bank is seen as a more trusted brand that many of its rivals.”