The firm cited "the impact of the current economic environment, the worsened outlook for economic growth and the increasingly regulatory requirements of the financial services sector in general" as reasons for withdrawing.
The sale, known as Project Verde, was a European Commission requirement in return for Lloyds receiving state help in 2008.
The deal with the Co-operative Group was first agreed upon in June 2012 but was awaiting approval from the respective Boards and regulators.
Lloyds said it now intends to dispose of the branches via an Initial Public Offering (IPO) and rebrand them as TSB Bank.
This will operate as a stand-alone bank within the Lloyds Banking Group.
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Antonio Horta-Osorio, chief executive of Lloyds Banking Group, said: "We are disappointed that 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 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."
Peter Marks, group chief executive of the Co-operative Group, said: "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.
"We were, however, clear from the outset that Verde was a complex transaction and that this was not the only option open to us to develop our Bank."

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