The former Labour financial services secretary had been appointed to review the group’s business structure and has faced criticism from senior members over his plans to reform the business.
Patrick Gray, president of the the Co-op’s largest independent society, Midcounties, told the BBC’s Today programme on Wednesday that “if Lord Myners puts forward simply a menu on a take it or leave it basis, then we will vote against it.”
Despite the announcement of Lord Myners’ resignation, the Co-op says his review will remain ongoing.
The BBC report says Lord Myners claimed in his review that elected directors had overseen “breathtakingly value-destructive” decisions including the takeovers of Britannia building society and the Somerfield supermarket chain.
He has also said that too many of the group’s directors had insufficient business experience and as result were not equipped to supervise senior managers.
Lord Myners’ recommendations include the appointment of new group board directors against clear criteria of skills and experience.
He has also proposed changing the board structure from the current 20 elected directors to one consisting of an independent chair, six or seven non-executive directors with business experience and two executives from within the Group.
Co-op Bank this week admitted that it had not yet reclaimed millions of pounds paid out as bonuses to senior executives Neville Richardson and Barry Tootell, as it said it would following the revelation of a £1.5bn hole in its accounts.
Chief executive Euan Sutherland announced his own resignation last month, saying the company had become “unmanageable”.
Depite the ongoing problems, Co-op bank said in March that it plans to award significant pay rises to senior staff over the next two years – while also admitting it requires a further £400m in new capital to settle claims of past misselling of payment protection insurance and interest rate swaps.