A former Treasury official commissioned by the Co-op Group to examine how it incurred a £1.5bn financial black hole is being paid £2,000 a day by the debt-laden mutual.

Sir Christopher Kelly was handed the lucrative deal by Euan Sutherland, the Co-op chief executive who walked out last week when his pay arrangements were leaked to this newspaper.

Kelly was hired nine months ago to examine decisions made by the Co-op in the period leading to its discovery of a deep capital shortfall. He is expected to report in May. Sutherland walked out after 10 months, branding the organisation "ungovernable". His departure followed a report in the Observer that revealed details of his £6.6m pay deal for 2013 and 2014. The revelations also prompted Sutherland to launch a blistering attack on "an individual or individuals" trying to undermine him in a posting on the group's Facebook page.

The episode seemed to confirm concerns by some within the Co-op over how its management was responding to recent crises. In December the Observer revealed that the Co-op was cutting funding for ethical causes while spending thousands on Quiller Consultants, a lobbying and reputation management firm. Quiller is led by Sean Worth, a former adviser to David Cameron, along with, until recently, George Bridges, a former Conservative campaign director and close friend of George Osborne.

Another contentious issue for many in the group was Sutherland's questioning of continued financial support for Labour MPs who also go under the mantle of the Co-operative party. The Co-op donates about £850,000 a year to Labour MPs. But it has now launched an online survey, which some claim presents leading questions designed to endorse a management decision to cut financial ties. Among the questions, is: "To what extent do you think it is appropriate or inappropriate for big business to donate money to political parties?"

Gareth Thomas, the Labour and Co-operative MP for Harrow West and chair of the Co-operative party, said the group should abandon the survey. "The Co-op Group has had a particularly tough week and it will be more important than ever now that its management and members are able to pull together," he said. "Members have been voicing significant concerns about the motivation, methodology and drafting of the 'Have your say' survey and the signals it sends about the group's future direction on key issues, including the member dividend and its political engagement."

"Acknowledging this concern by de-prioritising, or even abandoning, the survey would be one way to rebuild trust and would be a shrewd move that I hope [interim chief executive] Mr Pennycook will consider."

Defending the virtues of mutuals, Jon Cruddas MP, head of Labour's policy review, writes on the Observer website: "At stake is the Co-operative party, which has a deep historical link with the Labour party." A source close to the management insisted that the questions in the survey were not leading, but said that an organisation in such a financial mess did need to reconsider its spending.

On Friday former City minister Lord Myners, who was appointed a non-executive director of the group's pharmacies, supermarkets and funeral homes after the finance problems emerged, said the Co-op needed to take immediate action to reform, or risk its future.

In a report on how it should reform, he said: "There is a phrase frequently used in Co-operative Group circles that the executive should be 'on tap but not on top'. It is now clear to me that this is a widely held but deeply flawed representation of the reality in recent years. Elected directors have simply not been up to their task of holding the executive to account." He proposed a new board with an independent chair, six to seven independent non-executive directors, and a national membership council of 100 individuals, to make sure the group adhered to co-operative values.

A spokesman for the Co-op said: "The work of Sir Christopher Kelly and his team is vital in identifying the truth of what went wrong at the Co-operative Group and Bank and restoring our integrity. It is only with such detailed knowledge that we can rebuild and move forwards. This independent inquiry, which is being carried out in a professional and forensic manner, is an essential investment in the future."