The Treasury will be asked to look at whether or not Bradford & Bingley could be resurrected and returned to the high street to provide greater competition, a minister said.
It comes after MPs lobbied the Treasury to release documents revealing why the building society-turned-bank was nationalised and broken up at the height of the financial crisis.
Financial Secretary Sajid Javid was replying to Conservative MP Philip Davies (pictured) who had asked: "Will you go away and think about whether or not a new Bradford & Bingley could be borne out of what is there at the moment, to be a new challenger on the high street to the the banking sector, to introduce the competition that we all want to see?"
Responding on behalf of the Government, Mr Javid said: "I will commit to you that I will think about that further and I'll do more."
Mr Javid said he would write to the head of UK Financial Investments (UKFI), the Treasury unit that manages the Government's stakes in banks, "and ask them to consider your comments and the case that you have made today during this debate".
But despite suggestions that officials were purposefully blocking the publication of records on Bradford & Bingley, Mr Javid dismissed suggestions that the previous Labour administration had failed to follow due process.
MPs heard that one million Bradford & Bingley share and bondholders, as well as many employees, were still in the dark about why the bank was broken up.
Mr Davies said that the local community had "lost a highly valued brand from the high street, one that was in existence since 1851".
He said the then Labour prime minister Gordon Brown's decision to nationalise Bradford & Bingley in 2008 was "extremely disappointing" for the shareholders, many of whom remain outraged by what they consider to be "legalised theft".
Despite admitting in 2011 that it did possess relevant records regarding the decision to nationalise the bank, the Cabinet Office has refused to release them on the grounds of public interest.
Mr Davies said: "Surely the public interest demands full disclosure of the facts in order to secure the truth in this matter? How can the refusal to release whether or not the nationalisation of Bradford & Bingley was ever ratified by the Cabinet ever be in the public interest in a democracy?
"Surely voters are entitled to know this, let alone shareholders, bondholders and employees?"
He added: "Why was Bradford & Bingley uniquely closed down, especially given that its financial situation was certainly no worse, indeed all the evidence suggests it was better than the others."
Turning to Mr Javid, he said. "Whatever the reason and however little we like the reason, I hope you agree that we're entitled to know the reason."
He went on: "An independent inquiry into the nationalisation of Bradford & Bingley is long overdue. The Bradford & Bingley shareholder, bondholders, employees and the local community are entitled to know the truth."
He challenged the Prime Minister, saying if he was serious about his commitment to transparency then this was his opportunity to prove that.
"The Prime Minister has claimed many times his commitment to open and transparent government and has opened an inquiry into the Co-op bank failure," said Mr Davies.
"I believe it's not too late for the Government to do the same. That is, open an independent inquiry in respect of the Bradford & Bingley nationalisation, as this was arguably the best example of what went wrong in the banking crisis.
"Justice and the British sense of fair play demand such action, and I hope that you, minister, a good man, will do the right thing and agree to it.
"The Government rightly claims to want to be on the side of hard-working people; it's hard-working people who are the shareholders, bondholders and employees of Bradford & Bingley who all lost out."
Joining calls for a public inquiry, Calder Valley MP Craig Whittaker said: "When a government confiscates the property of its citizens without reason, explanation or compensation, particularly when it has a duty of care to their citizens, surely this alone has to be the reason to call for an independent inquiry into what happened?"
Mr Javid said: "After conducting a robust and rigorous process the independent valuer determined that no compensation was payable.
"I believe that due process has been followed at every stage, transparent and independent arrangements for compensation have been put in place and there has been a proper process through the courts.
"I'm not persuaded that there is a case for a further inquiry."
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