Donald Trump's lawyers have threatened to sue Britain's national broadcaster for $US1 billion ($1.5 billion) over the edit of a "salacious" documentary that's plunged the organisation into crisis.

A letter dated November 9 and signed by one of Mr Trump's lawyers, Alejandro Brito, claimed "fabricated" statements aired by the British Broadcasting Corporation (BBC) last year had caused the US President "to suffer overwhelming financial and reputational harm".

The BBC's director general Tim Davie resigned on Sunday and conceded the broadcast in question, an episode of its Panorama program which aired in the lead-up to last year's US presidential election, was "misleading".

The organisation has been in damage control since the edit was thrust into the spotlight when a leaked memo detailing

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