Former City minister Lord Myners wants to replace this with a slimmed-down "plc and beyond" structure staffed by professionally-trained directors.
The former Marks & Spencer boss was appointed a director of the Co-operative Group in December but announced he is to leave following this weekend's vote.
He has said it was apparent to him from the first time he attended a board meeting that not one of its members had the ability to address the complex issues faced by a group burdened with £1.4 billion of debt.
This weekend's ballot will be decided by representatives of its independent societies and affiliated organisations - who hold 22% of the vote - and others voting on behalf of its regional membership boards making up the remaining 78%.
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A Met Office warning covering much of England and south-east Wales is expected to remain in place until 11am.
A band of cloud and patchy rain is expected across Scotland and Northern Ireland, moving southeast as the day progresses.
Charity warns an estimated 30 child refugees a day are being expelled from EU countries after crossing the border from Serbia.