Lloyds Banking Group today named the Co-operative as its preferred choice to buy the 632 branches it is selling under European competition rules.
The taxpayer-backed bank will now enter into exclusive discussions with the Co-op, which beat off competition in the auction from NBNK Investments, a takeover vehicle run by former Northern Rock boss Gary Hoffman.
The sale update came as Lloyds said chief executive Antonio Horta-Osorio would return to his job on January 9 after a period off work with exhaustion.
Lloyds is being forced to divest the branches because of the £20 billion in state aid it received following the 2008 financial crisis.
The assets being sold account for a 4.6% share of the UK current account market and up to 19% of the group's mortgage book. There are five million customers and an estimated 9,000 employees.
The disposal plan - dubbed Project Verde by Lloyds - is seen as a way of introducing a stronger challenger to the big five banking groups.
The bids by the Co-op and NBNK are thought to have been in the region of £1.5 billion, but the Co-op was seen as slight favourite because it already runs a sizeable bank.
It acquired Britannia in 2009 and currently has 343 branches and 6.5 million customers, including in current accounts, mortgages and credit cards.
Co-op chief executive Peter Marks said: "We think a combination of these branches and our own would significantly strengthen our position as a real challenger in relationship banking in the UK."
Virgin Money, which recently secured Northern Rock for £747 million, was also reportedly involved in the auction.
The decision to start exclusive talks with the Co-op did not involve Mr Horta-Osorio, who has been on leave since the start of November.
Lloyds said it completed a rigorous process, including independent medical advice, before deciding its chief executive was fit to return.
It has pledged to strengthen the roles of its senior management team to reduce the day-to-day pressures on Mr Horta-Osorio.
Group finance director Tim Tookey filled in as chief executive and the company lined up board member and former Barclays executive David Roberts as a potential stand-in if Mr Horta-Osorio's return was delayed.
Lloyds has until November 2013 to complete the Verde sale.
Mr Marks stressed the Co-op would only proceed with a deal if it was in the interests of its members and other stakeholders. It is mutually owned, with profits shared between members and also used to invest for the long term.
The Building Societies Association said it welcomed the potential expansion of the mutual sector in the banking market.
Director general Adrian Coles said: "Quoted banks often put the interests of shareholders above those of customers.
"All of our research shows that mutuals offer a better customer service - this change will markedly increase the number of branches in the high street that are more interested in customer service than shareholder return."
Business Secretary Vince Cable said: "If successful, the bid will create a substantial new presence on UK high streets for a mutually-owned bank with high ethical standards and a track record of good service to customers. This will boost competition and the choices available to both consumers and businesses.
Virgin Money will take a presence in the mortgage market for the first time as its Northern acquisition has fuelled hopes that it will be a stronger challenger to the dominant banks. It plans to launch current accounts in 2013.