Flagship BBC news shows including Newsnight and Radio 4’s Today are to be subjected to the same cuts that have led to plans to axe Victoria Derbyshire’s BBC2 show.

Next week the corporation will announce it is looking for cost savings of about £40m in its news division, a move that will hit even key shows such as Radio 4’s The World At One.

It is understood the efficiencies being planned include Newsnight being asked to make fewer films. The late night BBC Two show is renowned for its agenda-setting coverage, last year broadcasting Emily Maitlis’ exclusive interview with Prince Andrew.

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BBC Radio will be expected to share resources and material across its bulletins on different stations. At present, they have bespoke news roundups.

More presenters will also be asked to work across programmes and channels.

The changes are being proposed because BBC News has to save £80m as part of a pan-BBC efficiency target of £800m to help pay for free TV licences for over-75s.

It has already saved half of that through moves such as axing politics show This Week. However, last year the director of news and current affairs, Fran Unsworth, told Television magazine the savings required for the next £40m would be even more noticeable. “I think they [viewers] will see it this time. We are looking at our whole operating model,” she said.

A key part of the cuts, which will be announced on Wednesday is, as Unsworth put it, making “the material go further across outlets … [through] more sharing of material across the board but that’s always a difficult thing to achieve in the BBC because we’ve got a lot of services – they all like to do their own thing.”

Meanwhile, after it emerged earlier this week that Victoria Derbyshire’s morning current affairs programme appeared to be the major casualty of the cuts, an online petition was set up to save the show. It had reached about 12,000 signatures by Friday.

The award-winning show, broadcast on BBC Two and the BBC News channel, has been praised for its investigations and diversity. The BBC itself praised its team in its 2018-19 annual report for “taking the show and viewers into locations rarely explored on television”. However, its cost versus its relatively low ratings – its audience average is 223,000 so far this year – put it in the line of fire, although there are suggestions it could continue online.

A former senior BBC executive said the corporation is in an impossible position. They said: “People want it to be smaller but they also want to keep the bits they like. The scale of the cuts being asked now means that the strategy of salami slicing budgets is no longer enough. Whole programmes and services have to go. This is the cost of delivering free TV licences to over-75s.”

There is also the thorny issue of the cost of compensating for unequal pay, with payouts recently being made to Samira Ahmed and Sarah Montague.

Against that background, the BBC is also being asked to cater more for younger audiences who are getting their news from other sources. Regulator Ofcom’s review of BBC news and current affairs output said in October: “The BBC is struggling to engage younger audiences with news, particularly online.”

The BBC declined to comment.