The joke, broadcast on Radio 4, mocked the Government’s White Paper that was released to MPs on Thursday.
Accusing the Prime Minister of a rushed job, the radio programme slated her efforts, likening it to a school “collage”.
Theresa May's Brexit White Paper was mocked on Radio 4's The News Quiz
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It had the whiff of a sixth form project
But, the sensitive gag left a sour taste with some listeners, who blasted the impartial broadcaster for its “left-wing bias”.
Airing on Friday evening, the satirical panel show took digs at the Government’s gaff and Mrs May’s efforts for taking Britain out of the crumbling bloc.
Comedian Miles Jupp said: “It was essentially a speech that she had already given just transcribed and put on this thing.
“It says things like ‘the precise form of this agreement will be the subject to negotiation’ – it was, I think it’s fair to say, pretty vague – it had the whiff of a sixth form project.”
Miles Jupp and Susan Calman made digs at the prime minister's plan
As the audience erupted into fits of laughter, fellow panellist Susan Calman chipped in with her take on the document.
“It’s like a collage of what Brexit means,” she sarcastically quipped.
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“Theresa May has done a mood board of what she wants everything to be – ‘now vote on that, there’s lots of purple, no blue or yellow, now vote on it’.”
The joke centred around a blunder in the White Paper regarding holiday entitlement
Although the panellist found their jokes at the expense of the Conservative leader humorous, some listeners took to social media to vent their outrage.
One annoyed person tweeted: “The left-wing rant that masquerades as The News Quiz. How is this politically biased show allowed to exit on the BBC unchallenged?”
Another raged: “The News Quiz #comedy @bbcradio4 lots of laughs at the expense of #TheresaTheAppeaser”.
@BBCRadio4 The left wing rant that masquerades as The News Quiz. How is this politically biased show allowed to exit on the BBC unchallenged
— Rob Carson (@Rob__Carson) February 3, 2017
— Richard Baker (@bakerpictures) February 3, 2017
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Margaret Thatcher shares a joke with Ronald Reagan, at No. 10 Downing Street
The 30-minute episode also slammed Mrs May for her “slow response” in condemning Donald Trump’s temporary travel ban.
The panel suggested that a proposed state visit for the Republican should be blocked because of his “extremist views”, a week after he barred citizens from seven mainly Muslim countries entering the US.
Mr Jupp joked the Queen should “pretend to have double booked herself” to the embarrassment of Mr Trump.
While Ms Calman taunted that the US President should be allowed to fly into Britain, but then “refused entry because we do not allow people with extremist views into the country.”
Express.co.uk has contacted the BBC for a response.
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