The BBC would have to close 6 Music, axe its children’s programming or shut BBC One to cover the cost of losing a libel battle with Donald Trump , insiders warned.

The corporation has told the President’s lawyers that it will fight his lawsuit for up to $5bn (£3.79bn), claiming nobody in America watched its misleading edition of Panorama called “Trump: A Second Chance?” and that it did not damage his reputation.

Previous lawsuits with media companies in America ended with settlements of between £12m to £13m, and BBC insiders say even figures in that region could impact certain channels or services.

In a message to staff on Monday, under-fire BBC Chairman Samir Shah promised that the broadcaster would not back down, even if the row threatened a diplomatic rift between the Whit

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