The Andrew Neil Show will disappear from BBC schedules as part of cuts to the corporation's news operation.
The political discussion programme had already been off the air during the Covid-19 crisis and will not return. But the BBC said it was talking to Neil about a new BBC One interview show.
In total, 520 jobs will go, from a workforce of around 6,000 people.
That includes 450 job cuts that were announced as part of an £80m savings drive in January, and then put on hold.
Meanwhile, The Guardian has announced that it will cut 180 jobs, including 70 from editorial teams.
Which other BBC programmes will be affected?
Most of the changes will take place behind the scenes.
The corporation's head of news, Fran Unsworth, said the BBC would concentrate on fewer stories, with journalists pooled in centralised teams, rather than working for specific programmes.
The BBC News Channel and BBC World will continue to share some output in the mornings and evenings, as they have done during the Covid-19 crisis, although they will remain separate channels.
Radio 4 programme In Business will close, as will the Business Live page on the BBC News Website, while bespoke business news bulletins on the BBC News channel will be reduced.
On BBC World Service, World Update and The World This Week will end, while daily current affairs show Newsday will shorten in length.
One of Neil's former programmes, lunchtime TV show Politics Live, will return four days a week after being rested during the pandemic.
More than 100 MPs and peers recently wrote to the BBC, arguing that axing it permanently would "seriously harm the ability of the BBC to scrutinise and explain" politics.
How will the BBC cover stories?
The BBC says it will have fewer reporters overall, but that a new commissioning system (which was partly implemented during the Covid-19 crisis) will make sure coverage is better co-ordinated.
More interviews will be conducted by Skype, Zoom and other video technologies, meaning there's less reliance on satellite trucks and radio cars.
A new original journalism team will also be created, incorporating several staff from the Victoria Derbyshire show, to pursue under-reported and exclusive stories. There will also be a greater focus on digital storytelling.
Unsworth said Covid-19 had "changed all of our lives" and had also "led us to re-evaluate exactly how we operate as an organisation".
She said: "Our operation has been underpinned by the principles we set out earlier this year - fewer stories, more targeted and with more impact. For BBC News to thrive, and for us to continue to serve all our audiences, we have to change."
After the announcement, the corporation revealed that legal correspondent Clive Coleman has decided to leave the BBC at the end of the year.
Why are the cuts being made?
The BBC announced in 2016 that it needed to save £800m, with around £80m of that figure coming from News.
Just over £40m - around half of the savings required - has been found over the past four years.
In January, the corporation announced plans to close 450 jobs, as well as programmes like BBC Two's highly-regarded Victoria Derbyshire show.
The cuts were later postponed as the newsroom faced the demands of covering the coronavirus pandemic.
At the same time, the BBC delayed a decision to end free TV licences for the over-75s. That contributed to a further budget shortfall, meaning that the number of proposed job losses in news has increased by 70 posts.
A separate decision to cut 450 jobs in the BBC's regional newsrooms was announced earlier this month.
What next for Andrew Neil?
Neil has been one of the BBC's top political broadcasters over the past two decades on shows like This Week and Daily Politics.
The Andrew Neil Show began in autumn 2019 in the run-up to the general election and the UK's departure from the European Union. It included interviews with most party leaders, but Prime Minister Boris Johnson did not appear - leading the host to controversially deliver an on-air ultimatum.
Announcing the latest cuts, the BBC said: "We remain committed to Andrew Neil's in-depth interviews (as well as the Budget, US Election and other Specials).
"The Andrew Neil Show will not be returning but we're in discussions about a new interview series on BBC One."
Neil had previously told the Radio Times he feared he would become "surplus to requirements" as the BBC made cutbacks.
Today we have fresh details on the radical experiment that BBC News announced in January.
Two big things have changed because of coronavirus. It has accentuated the BBC's financial strain, and shown a different way of working is possible. Both help account for the rise in likely redundancies.
The fact that Politics Live will come back for four days a week will appease many in Westminster - but the loss of The Andrew Neil Show will have the opposite effect. That show was originally commissioned because of an intervention by Tony Hall, but he is leaving as director general in September.
The BBC says Neil's in-depth interviews are still key to its coverage, and they would like to find a slot on BBC One for those interviews.
There is no one correct way to conduct interviews. The right approach depends on the interviewer, the interviewee, and the context.
But in one particular style - forensic, unrelenting scrutiny and interrogation of those in power - Neil is the best in the business.
His talks with the BBC are far from resolved. Two fresh proposals have run aground. He will no longer do Politics Live - but has been approached by other broadcasters.
What's the reaction?
Broadcasting union Bectu said it would hold BBC management to account and seek to avoid compulsory redundancies.
"BBC News is one of the most trusted brands at home and abroad. In an era of fake news and during an unprecedented health crisis this trust in a public service broadcaster is critical," said Bectu head, Philippa Childs.
"The government needs to take back responsibility for free licence fees for the over-75s, providing precious resources that would allow BBC News to continue to provide its world-leading range of news broadcasting."