Shai Masot, a political officer at Israel's British embassy has been secretly filmed planning how to "take down" certain British politicians.
The film was shown on Al Jazeera, the Qatari government-owned media network. The film is from last October.
In the film he discusses "idiot" Boris Johnson, and how to "take down" his deputy Sir Alan Johnson. The Israeli ambassador has apologised on behalf of his political officer.
Sir Alan described Israeli settlements in 2014 as "illegal", and is often critical of Israel's expansion into the troubled west bank.
The film is shot in a restaurant, in which Mr Masot asks, "Can I give you some names of MPs that I would suggest you take down?" He is dining with Maria Strizzolo, an aid to education minister, Robert Halfon. Halfon was the former director of Conservative Friends of Israel.
Ms Strizzolo, who according to Al Jazeera, said all MP's have "something they're trying to hide".
Talking about Boris Johnson, he said, "He's basically good. He just doesn't care. He's busy with everything else.
The Israel Embassy issued a statement, saying it "rejects the remarks concerning Minister Duncan, which are completely unacceptable.
"The comments were made by a junior embassy employee who is not an Israeli diplomat, and who will be ending his term of employment with the embassy shortly.