A letter sent to BBC director general Mark Thompson, seen by The Guardian, accuses Paxman of losing control of the show after studio guest and journalist Peter Oborne described Amadeu Altafaj Tardio as "that idiot in Brussels".
Paxman eventually admonished Oborne, a commentator for The Daily Telegraph, for being "gratuitously offensive", but by then he had repeated the phrase several times in a debate on the eurozone crisis.
It was also not enough to stop Tardio, speaking via video link from the BBC's Brussels studio, from walking out of the interview.
Watch a video of the incident below:
The letter from EC commissioner Olli Rehn, which was copied to the BBC Trust chairman and former EU commissioner Lord Patten, said that Paxman failed to make it clear quickly enough to Oborne that his first insult was completely inappropriate.
"I was shocked by such an unacceptable behaviour as Peter Oborne's being effectively endorsed by a top figure of the BBC," said the letter.
"When Mr Paxman finally reacted, after tolerating those insults several times, using the same 'idiot' language himself and having lost control of the programme, it was too late.
"The abused commission spokesman, who showed enormous patience and commitment, considered it was useless to try to have a rational discussion with interlocutors that resorted to insults instead of intelligent arguments, and took the right and difficult decision to leave. A shame, and improper practice for the BBC."
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