Senior Tory minister says public broadcaster must regain public trust after recent scandals if it wants to maintain the status quo

The BBC could face a cut in the licence fee or even have to compete with other broadcasters for a share of the money unless it rebuilds public trust and becomes more transparent, a senior Conservative minister has suggested.

Tory chairman Grant Shapps told the Sunday Telegraph the BBC must tackle a culture of secrecy and waste in the wake of the Jimmy Savile and Stuart Hall scandals and rows over stars' salaries and pay-offs to senior executives.

And he said there was a "question of credibility" for the BBC over whether it applied "fairness" to its reporting of politics.

With the BBC's royal charter coming up for renewal in 2016, Shapps suggested there were "lots of different ways" in which licence fee-payers' money could be used to fund public service broadcasting.

And he said the £145.50 annual fee would be "too much" if the BBC failed to reform.

Shapps is not a full cabinet member, but attends weekly meetings in his role of minister without portfolio, and is regarded as a rising star in David Cameron's team.

He made clear Conservative frustrations with the operations of the BBC.

"They have ended up working in this culture which is buried in the last century, which is 'we are the BBC, we do what we like, we don't have to be too accountable'," he told the paper.

"But they are raising £3.6bn through the licence fee, which is a tax, and, quite rightly, the public wants to have sight of how the money is spent. Things like the pay-offs have really caused concern, as have, obviously, things like Savile and Hall and the culture that goes around that. I think it is one of too much secrecy."

He said the BBC director-general, Lord Hall, should consider opening the corporation's books to full inspection by the National Audit Office, publishing all expenditure over £500 – including stars' salaries – and opening up to freedom of information requests.

"In order for the public to have confidence in the three-and-a-half billion plus that is given to the BBC – compulsorily, just because you have a television – and to move beyond Savile and the pay-offs and all the rest of it, the only way they can do that is to really go for a much more transparent, open deliberate policy," the Tory chairman said.

"If they do that they can make sure they win back public trust. If they don't, they are in danger of frittering away Auntie's public trust that has been built over a long time."

He indicated he was ready to contemplate changing the system that gives the BBC all the money raised through the licence fee.

"People pay their licence fee in this country because people believe that we should have public service broadcast programming," he said. "Of course, there are lots of different ways you could do that.

"I would also say that £145.50 is quite a lot to pay for everyone in the country who has a TV. It is too much if we don't see the kind of reforms that all public organisations are used to that the BBC isn't having to engage with as much as it could do."

A BBC spokesman said: "Mr Shapps is right that transparency is key to the future of the BBC. So is its freedom from political pressure.

"The BBC and the BBC Trust actively encourages the public to tell us what it thinks of our services and help us police our own guidelines. On TV and radio they personally hold its executives to account.

"In 2012 the BBC dealt with more than 1,600 freedom of information requests and volunteered information on hundreds more. This year alone we have appeared in front of 16 parliamentary committees, while the NAO already has full access to the BBC's operations except its editorial decisions.

"We are proud of the quality of our news and its commitment to reporting without bias. Where we believe or are shown to have erred we correct and apologise."

The spokesman defended a feature by home editor Mark Easton on a recent European Commission report about immigration, which Shapps maintained was "wrong".

"We are satisfied that our coverage of the European Commission report was fair, balanced and impartial," the BBC spokesman said.

"As we do with all our stories, we explored the wider debate with relevant context and represented a range of views. Mark Easton is one of our most experienced and well-respected journalists with a long track record in reporting without fear or favour."