The BBC was warned on Monday that it is facing a “dangerous moment” as Conservative MPs seized on the departure of director general Tony Hall to call for an overhaul of its funding model and an end to the licence fee.

John Whittingdale, the former culture secretary, led calls for a debate on the BBC’s funding model to start as soon as its mid-term review in 2022, arguing that Hall’s replacement would have to consider how the broadcaster can compete in the Netflix era.

The Tory MP, who negotiated the 2016 charter renewal and is tipped for a possible return to his old job in the reshuffle, told the Guardian: “The massive increase in streamed content and the proliferation of subscription services does raise questions about the sustainability and how we continue to support public service broadcasting generally and also the future of the licence fee.”

Hall is due to step down in the summer after seven years in the job, having been brought in to stabilise the broadcaster after the Jimmy Savile scandal in 2012. In an email to staff he announced he was leaving to take over as chair of the National Gallery.

He said: “The BBC has an 11-year charter – our mission is secure until 2027. But we also have a mid-term review process for the spring of 2022. We have to develop our ideas for both. And it must be right that the BBC has one person to lead it through both stages.”

His successor will have to steer the broadcaster through ongoing controversies over equal pay, disputes, political bias and diversity. However, the new director general’s biggest battle is likely to be over the corporation’s funding, after Boris Johnson hinted during the election that he thought the licence fee may no longer be a sustainable model.

The BBC board, rather than the government, will pick Hall’s successor but several senior Labour figures warned that the BBC in its current form was looking vulnerable.

Facebook Twitter Pinterest Hall said it was important that the same person was in post for the BBC’s mid-term review and its charter renewal in 2027. Photograph: Ben Stansall/POOL/AFP via Getty Images

So deep are the anxieties about the corporation’s direction that some viewed the timing of Hall’s departure as designed to ensure that the current BBC chair, Sir David Clementi, would pick his successor rather than a new chairman picked by the government. A new chair is due to be recommended in February 2021.

Harriet Harman, the former shadow culture secretary, said the broadcaster was facing a “dangerous moment” with many Tories not committed to a public service broadcaster at all, while Kevin Brennan, the shadow media minister, said the new director general would have to be prepared to defend the organisation against “a very rightwing government with some voices who would want to break up the BBC”.

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Whittingdale said replacing the licence fee with a subscription service would be “some way off” because it would only be possible when television is distributed over the internet. But the possibility of moving to a subscription was “a debate which it is sensible to begin to have certainly at the time of the mid-term review” because it could be a live discussion for years.

“I had a very good relationship with Tony Hall. I think he’s done a good job. We had a robust negotiation but we ended up with a charter that was good for the BBC. But even though the renewal only took place three or four years ago, the world has changed a lot,” he said. “We wrote into the charter, against the BBC’s wishes, a mid-term review in 2022. Although that was primarily about the new governance structure, it does provide an opportunity to at least begin the debate about the future of the licence fee.”

A string of Tory critics of the BBC said any new director general would need to be open-minded to new ways of funding the broadcaster. Andrew Bridgen, a Tory backbencher, said the last charter review “didn’t grasp the nettle of online streaming” and called on the BBC to stop “clinging to the licence fee like it is a life jacket when actually it is the stone that is dragging it down” by stopping it tapping into a global market for its services.

Another Conservative MP Julian Knight, who is running to be chair of the Commons media committee, said the election had given the party a second chance to reform the BBC after failing to do so at the last charter review.

He said the government “must seize the opportunity created by our victory to help the BBC transition to a new model, one which retains that which makes it such a unique and beloved institution but weans it off the poll tax and fosters a culture which is more open to commercialism and accessible to outside talent.”

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Damian Collins, who chaired the Commons media committee until the election, did not agree with scrapping the licence fee but suggested the BBC needed to review the way it raises its money.

“The BBC is in a tight spot and will have to work harder to keep the engagement and trust of licence fee payers,” he said. “I think you could look at ways for the BBC to increase its revenue from subscriptions such as programmes that have dropped off the iPlayer or having international subscription to the iPlayer.”

But Ben Bradshaw, a former culture secretary, warned the government to “think very carefully before doing anything hasty” with the BBC’s free-to-air funding model.

“There is always going to be a debate about the BBC’s funding but in an era when there is growing concern about fake use and the misuse of data by powerful corporations, hostile powers, political parties and campaigning organisations, the case for a trustworthy, objective and accountable news provider is as strong if not stronger than ever,” he said.

Names being mentioned as potential candidates to take over from Hall include Sharon White, the former chief executive of media regulator Ofcom; Gail Rebuck, the chair of the publishing giant Penguin Random House; and the Channel 4 chief executive, Alex Mahon.

Possible internal candidates include the BBC’s director of content, Charlotte Moore; its director of radio and education, James Purnell; and the director of news and current affairs, Fran Unsworth.

The chair of the National Gallery has been vacant since September last year when Hannah Rothschild stepped down.

“It’s been such a hard decision for me,” Hall wrote in an email to staff on Monday. “I love the BBC … If I followed my heart I would genuinely never want to leave.” Hall said he would continue to work flat out “to demonstrate why public service broadcasting – with the BBC at its heart – is an eternal idea”.