The branch sale, known as Project Verde, is a requirement imposed on Lloyds by the European Commission as part of the bank receiving state aid in 2008.
Lloyds says it will now look to dispose of the branches through an initial public offering, subject to regulatory and European Commission approval.
The branches will rebrand as TSB Bank in the summer, and will operate as a separate business with Lloyds.
Lloyds chief executive Antonio Horta-Osorio says: “We are disappointed The Co-operative Group is unable to complete this transaction. However, we are well advanced in our plans to bring the Verde business to the UK high street during the summer through the TSB Bank, and will now proceed with the option to IPO the business, subject to the necessary approvals.
“The TSB Bank will be an attractive retail and commercial bank that will have around 630 branches across the UK, a strong management team and will be a real challenger on the high street.”
The Co-op Group chief executive Peter Marks says: “After detailed and thorough consideration of all aspects of the Verde transaction, we have decided, at this time, that it is not in the best interests of our members to proceed with the transaction.
“Having worked closely and constructively with Lloyds we are naturally disappointed to have reached this conclusion.
“However, against the backdrop of the current economic environment, the worsened outlook for economic growth and the increasing regulatory requirements on the financial services sector in general, the Verde transaction would not currently deliver a suitable return for our members within a reasonable timeframe and with an acceptable level of risk.”