The bank had to be rescued by bondholders and is now majority-owned by hedge funds and other investors. In November the bank's former chairman, Paul Flowers,whose embarrassing lack of financial knowledge had already been exposed, was filmed allegedly buying drugs.
Lord Myners was brought on board by the Co-op group in December, having said that its "failed" board needed to take responsibility for the mistakes at the bank.
However, the reform efforts suffered a blow in March when Euan Sutherland, chief executive, resigned after just 10 months, calling the group "ungovernable".
Read MoreCo-op bank boss quits after debt rating downgrade
Lord Myners expressed sympathy for Mr Sutherland at the time and said the 21-strong board of mostly elected lay members – including a farmer, a plumber and a nurse – should be replaced by a smaller group of professional directors, an independent chairman and two executives. Elected members would form a 100-strong body to enforce the group's ethical principles.
However, the plan has provoked a backlash by activists among the Co-op's 7m members. Many argue such an approach would turn the Co-op into a PLC and force it to shed its ethical principles. Changes to the group require a vote by two-thirds of the members of regional committees. The Midcounties Co-op, and several others, have already voted against the Myners reforms.
A public consultation campaign asking whether the group should stop its funding of the Co-operative party, allied to Labour, has further inflamed opinion among some activists.
More from the Financial Times:
Co-operative Group shakes up management team as losses loom
Co-op is shaken, not the mutuals' model
Myners proposes Co-op Group board shake-up
The Co-op Bank is set to report big losses when its delayed results are announced this week. It requires an additional £400m to cover the cost of mis-selling scandals with the Co-op needing to contribute £120m to prevent its stake in the bank falling below 30 per cent.
Richard Pennycook, a former Wm Morrison finance director, is the acting chief executive. Some activists want him to turn down a proposed retention package for 2013 and 2014 at the annual general meeting in May.
Follow us on Twitter: @CNBCWorld