Mann said on Friday the decision to exclude him and the Conservative MP Andrea Leadsom from the Treasury committee was taken because they were outspoken, and he accused Andrew Tyrie, the chair of the official committee, of "reaching his conclusions in advance".
Tyrie, the Tory MP who chairs the Treasury select committee that is investigating the Barclays Libor scandal, has agreed to chair the inquiry committee on the basis that it had cross-party support after Labour's attempts to call for a full public hearing.
The MPs on the committee also sit on the Treasury select committee – Conservative Mark Garnier, Labour's Andy Love and Pat McFadden, and Liberal Democrat John Thurso. Lords will be appointed to the committee as well.
Mann is angry at being excluded from the inquiry. He said: "Both Andrea and I were available for the inquiry and because we are too outspoken we have been blocked. This exposes the inquiry as a total whitewash, with Andrew Tyrie reaching his conclusions in advance of the meetings. We need to get to the bottom of this scandal and I'm therefore setting up my own inquiry into this dreadful mess."
Speaking to the Guardian, Mann claimed the Tyrie inquiry would not "get to grips" with the key issues, partly because it has already nearly completed an investigation into corporate governance.
"Is it going to look in detail at what's being going on at RBS and HBOS?" he asked. "Is it going to work hand in glove with the Congress and Senate inquiries? Is it going to be taking evidence from people in the US who are well ahead of the game on this? Is it going to look at the EU proposals on this?"
Mann said he was concerned that the three most "independent-minded" Conservatives on the Treasury committtee – Andrea Leadsom, Jesse Norman and David Ruffley – had not been included on the new commission.
It was particularly odd that Leadsom, "who has proven to be her own person, knowledgeable and prepared to challenge", was left out, he said.
He claimed that the way the committee was set up was "an absolute dream" for Ed Miliband, because it confirmed the Labour leader's warnings about a parliamentary inquiry being unsatisfactory.
The Bassetlaw MP said he had already started work on his own report. He has two researchers helping him, but said he hoped get more help: "There's lots of goodwill out there, including people in the banking industry."
Asked if his inquiry would take evidence in public, he said: "We will look at the timescale and see what's possible."
It is understood that MPs were selected on the advice of their parties.
A motion to set up the committee has the support of the prime minister, David Cameron, the deputy prime minister, Nick Clegg, the chancellor, George Osborne, Miliband, and the shadow chancellor, Ed Balls.
The inquiry is scheduled to report on 18 December – raising speculation that it may need to met during the summer recess.
The inquiry will be able to seek advice from lawyers, to distinguish it from a traditional select committee. It will look wider than the scandal sparked by the record £290m fine on Barclays for attempting to manipulate the inter-bank lending rate – examining professional standards and the culture of the banking industry.
Bob Diamond quit as chief executive of Barclays following a public outcry and pressure from regulators. The bank's chairman, Marcus Agius, will leave once a new chief executive is found.
Tyrie's Treasury committee will continue to hold hearings on Barclays next week, when Jerry del Missier, the chief operating officer who quit alongside Diamond, will appear. Officials from the Financial Services Authority are also being called, including its chairman, Lord Turner.
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