Tony Hall, the director general, will be questioned on the issue by the influential Culture, Media and Sport Select Committee next week, while the Women and Equalities Select Committee would also now debate the issue, its chair Maria Miller said.
Dozens of cross-party MPs have also written to the National Audit Office (NAO) demanding it too launch a formal inquiry.
The broadcaster stopped using so-called “gagging” clauses in 2013 in the wake of the Jimmy Savile scandal. But there are fears the BBC is using public money to fund court confidential settlements, known as non-disclosure agreements (NDAs), in order to keep allegations secret.
In a joint letter signed by 30 MPs including senior Conservative Nicky Morgan, the former Education Secretary, and parliamentarians from Labour, the SNP and the Liberal Democrats, they suggested the BBC’s use of the legal documents was “silencing the voices of victims”.
The letter said: “In our view the use of public money – collected from our constituents through the license fee – to conduct legal proceedings which pay off and silence victims whilst covering up wrongdoing would be wholly unacceptable and we feel that this matter must be investigated as a matter of urgency.”
Last night, the BBC confirmed that it continues to use settlement agreements that include confidentiality clauses to stop employees speaking out. It refused to disclose how many have been issued in recent years and said their use was “limited”.
Tory MP Damian Collins, chair of the Culture, Media and Sport Select Committee, told The Independent “the issue was likely to be raised” on Wednesday, while Ms Miller, a former Conservative culture secretary, said the use of NDAs was an issue “we should all be concerned about”.
“Across the board non-disclosure agreements are being used to silence people and stop them talking about their experiences within organisations,” she said.
“There is a real concern that these agreements are being used to disguise unlawful activities.”
She added: "Public bodies should not be using taxpayers’ money to potentially stop people talking about their experiences of behaviour that is unlawful."
Ms Miller suggested organisations could be forced to publish how many NDAs they have entered into, and criticised the BBC for refusing to disclose to The Independent how many settlement agreements it has utilised in recent years.
She added: “I think it’s unacceptable that an organisation like the BBC would refuse to acknowledge or make public how many settlement agreements they’ve entered into. Without that transparency it’s impossible to know the scale on which they’re being used.”
It comes after Downing Street announced Theresa May would look at the wider use of NDAs following the scandal over the Presidents Club dinner, at which numerous women allege they were sexually harassed. Many of the victims had been made to sign NDAs in relation to the event.
Speaking to The Independent, two former Conservative culture secretaries also raised concerns over the BBC’s approach.
In addition to Ms Miller, John Whittingdale said the BBC should not be using public money to silence victims.
“I’m very uncomfortable with the idea of the BBC enforcing non-disclosure agreements, particularly since I was the one who pushed for transparency over top salaries at the BBC”, he said.
“Any money paid out by the BBC is ultimately public money and I’m not comfortable at all with the idea the public aren’t being told how their money is being spent.
“If it falls within the remit of the National Audit Office, I’m sympathetic to the suggestion they should investigate.”
Mr Whittingdale also said it was right for the DCMS Select Committee to look at the issue. “If I was running the select committee this is something I would be looking at closely,” he said.
Labour’s David Lammy MP, a former culture minister who is co-ordinating the letter from MPs, said: “I was alarmed to read Carrie Gracie’s resignation letter and it is wholly unacceptable for taxpayers’ money to be spent on these legal proceedings, out of court settlements and agreements and there is a significant public interest in getting to the bottom of this issue.
“I fear that the widespread use of non-disclosure agreements in silencing accusers means that institutions can avoid facing up to wider, systemic problems at play here that must be tackled in a transparent and open manner.”
The BBC said it had not used a settlement agreement in relation to an equal pay issue for two years but confirmed the agreements are still used in relation to other disputes.
The BBC’s former China Editor criticised the use of non-disclosure agreements when she resigned from the role over pay inequality earlier this month.
In her resignation letter to BBC executives, Carrie Gracie, who is also appearing before the committee on Wednesday, wrote: “Speaking out carries the risk of disciplinary measures or even dismissal; litigation can destroy careers and be financially ruinous. The BBC often settles cases out of court and demands non-disclosure agreements.”
The Independent understands that former BBC employees who have signed NDAs believe they are only allowed to speak about their experience if forced to do so in court or when protected by parliamentary privilege, such as during a select committee appearance.
A BBC spokesman said: “The BBC hasn’t settled an equal pay claim raised by an employee with a settlement agreement for over two years. Since the pay disclosures last year, it’s been widely reported that a number of women have come forward raising queries about their pay. We have resolved a number of these, none of which has involved requiring confidentiality.
“The BBC also has clear processes so staff can raise any concerns about bullying, harassment and unfair treatment, and whistleblowers are protected by law even if they have entered into a settlement agreement.”
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