Former chairman Paul Flowers, a 63-year-old Methodist minister, was filmed talking about buying crystal meth, crack cocaine and ketamine by the Mail on Sunday tabloid newspaper in allegations published last weekend.
Flowers, also a former local councillor for the opposition Labour party, has since apologised -- leading to his subsequent suspension from the church and Labour.
A police statement released today said officers had last day "arrested a 63-year-old man... In connection with an ongoing drug supply investigation".
The lender and financial regulators are currently facing serious questions over his appointment, especially in light of the fact that the Co-op finds itself in a troubled financial state.
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Conservative Prime Minister David Cameron last day said that he would order a formal inquiry into the finances of the bank, which faces a big recapitalisation to cover bad loans and the costs of a failed expansion plan.
Flowers has meanwhile been engulfed in a highly damaging series of allegations over illegal drug use, sex with rent boys, drink-driving and questions over his expense claims while working for a drugs charity.
The revelations have sparked also the resignation of Len Wardle, who has stepped down as chairman of parent firm the Co-operative Group and who led the board that appointed Flowers three years ago.
The BBC today reported that Flowers -- who was paid 132,000 pounds a year -- resigned from the Co-op in June after being confronted by "lavish" expense claims, and growing doubts over his competence.