A sketch on Tracey Ullman’s BBC show in which the impressionist appears as Jeremy Corbyn and pokes fun at the row over antisemitism in Labour has provoked an angry reaction from some of the opposition leader’s supporters.

Some also erroneously blamed David Baddiel for writing the sketch, leading the writer and comedian to describe the accusations as “the weirdest conspiracy theory” he had ever seen. “Maybe I should ask for royalties. Or will that confirm the stereotype for the antisemites?” he said on Twitter.

The sketch aired on Friday as Ullman’s show – Tracey Breaks the News – returned for a second season in which the comedian once again donned a beige jacket and facial hair to impersonate the Labour leader. In the sketch, her Corbyn character is seen taking selfies with young men who he meets at a taxi rank outside an airport before a man in a skullcap and a black suit tells him that he wanted the Labour leader to do more about antisemitism in the Labour party.

“I hear you. I am all over it like cream cheese on a bagel ... it’s alright to say that, isn’t it?” Ullman’s Corbyn character replies.

Turning to the young men, he adds: “I want you to know that I am completely on top of all this Jewish stuff. I have spoken to every single antisemite in the Labour party and I’ve told them – in no uncertain terms – ‘tone it down a bit!’”

Dylan Strain, who describes himself on Twitter as an actor, writer and Corbyn supporter, said that the sketch was propaganda “slurring [Corbyn] as a terrorist sympathiser who is not bothered by antisemitism”.

However, Strain also brought Baddiel into the row in a tweet that was retweeted by George Galloway to his 289,000 followers: “I see @Baddiel wrote Tracey Ullman’s Corbyn sketch last night. More BBC propaganda masquerading as satire. Tip for Tracey – sitting in makeup for hours to look a bit like Corbyn is a waste of time if you can’t do the voice or mannerisms, or comedy.”

Strain later said he was being sarcastic and was suggesting that Baddiel could easily have written the sketch based on comments made recently about Labour and Corbyn on Frankie Boyle’s BBC show Frankie Boyle’s New World Order.

Baddiel said that he was initially puzzled when he became aware that people were tweeting about him and Ullman, before suspecting that it might be Corbyn supporters who had been angry at comments he had previously made on the Boyle show about antisemitism in Labour.

“Then it becomes clear to me – in an incredibly ‘Jew plus Jew equals seven’ way – that the Corbynistas had decided that I wrote this Tracey Ullman sketch,” he said.

“It does speak of something unconscious which is their sense that everything must involve elitist conspiracy, that it’s all connected and that anyone who they believe is trying to stop Corbyn getting into power must have links and be working together.

“The idea seems to be that if I have said something to call out antisemitism in the Labour party, then if there’s something or someone else doing that then I must be behind it in some way. At a deeper level, that speaks about myths of Jewish conspiracy, of Jewish control of the media etc.

“The problem is that even if Dylan Strain meant it as a joke, lots of people took it seriously, and because of the speed of social media, next thing you know George Galloway is saying it as if it’s fact – this all happens very quickly – lie and myth-making and what people want to believe about who the enemy are – it all becomes fact.”