Jo Brand's joke about throwing battery acid at politicians "went beyond what was appropriate" for a Radio 4 comedy show, the BBC has ruled.
The comedian came under fire for her joke on June 13, but the BBC ruled that it did not incite violence.
During an appearance on Radio 4's Heresy show, Brand - refering to politicians who had milkshakes thrown on them - said: "I'm thinking why bother with a milkshake when you could get some battery acid."
After making the comment, she said: "I'm not going to do it, it's purely a fantasy. But I think milkshakes are pathetic."
Ofcom has recieved 444 complaints about the episode, including one made through the BBC's complaints progress.
The TV regulator said it can only consider complaints if they have been through the BBC process first and if they complainant is disattisfied.
An Ofcom spokesman: "We are assessing the complaint against our broadcasting rules, but are yet to decide whether or not to investigate."
Following the broadcast, Brexit Party leader Nigel Farage, who just days earlier had had a milkshake thrown at him while campaigning in Newcastle, accused Brand of "inciting violence".
Commenting on Twitter, he said: "I am sick to death of overpaid, left-wing, so-called comedians on the BBC who think their view is morally superior."
The BBC's Executive Complaints Unit (ECU) said it did not uphold the aspect of complaints on incitement of violence as it had "considered the context in which the words were spoken".
A spokesman for the BBC said: "We note the findings and that the BBC's ECU concluded the comments did not condone violence and that no subject matter should be beyond the scope of comedy."
Scotland Yard said it was considering examining the case but did not take any further action.
It was believed the allegation reported to police was not made by Mr Farage or the Brexit Party.
The comedian apologised for the joke, calling it "crass and ill-judged", and the BBC removed the comment from its catch-up show.