The comedian Jo Brand will not be investigated further for a joke about throwing battery acid at politicians, the broadcasting watchdog has said.

Last June, Brand had joked on BBC Radio 4’s Heresy show, after milkshake had been thrown at several political figures by members of the public: “I’m thinking why bother with a milkshake when you could get some battery acid.”

The remark triggered a debate about the limits of freedom of speech, particularly in terms of satire, and the Metropolitan police briefly considered launching an investigation.

An Ofcom spokeswoman said: “Acid attacks are extremely serious crimes. We found that these comments had clear potential to offend listeners. But we also considered the audience’s likely expectations of Jo Brand’s style – and of this established show, which sets out to challenge accepted views in society through provocative comedy.

“We also took into account that Ms Brand immediately qualified her comments, making it clear they shouldn’t be taken seriously or acted upon.”

Responding to complaints after the show was broadcast last year, the BBC initially defended the comedian, but later said the remark was inappropriate for a Radio 4 comedy show.

The broadcaster dismissed claims from Nigel Farage that Brand was inciting violence. The Brexit party leader was doused with a milkshake in the run-up to the European elections.

The BBC added that jokes made on Heresy were “deliberately provocative as the title implies”, and were not intended to be taken seriously.

The Heresy show is billed as a “discussion programme which challenges established ideas and questions received wisdom”.

After making the comments, Brand immediately made clear she was joking and criticised the milkshake stunts. “That’s just me. I’m not going to do it,” she said. “It’s purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry.”

The comedian later apologised for making a “crass and ill-judged” joke.