Jo Brand will be back on Radio 4 next week, as police confirmed they will take no further action over her comments.
The BBC has apologised for offence caused after she said: “Why bother with a milkshake when you could get some battery acid?” in reference to people throwing cold beverages over politicians.
But the Telegraph understands that internally, the BBC are resolutely supporting the 61-year-old, with one insider saying: “Jo Brand is a much loved comedian and part of the Radio 4 family – she will continue to be so, and will continue to appear on our programmes.
She is next due on air on Thursday evening at 11pm with V.I.P. R.I.P. - a show which looks back on the lives of celebrities who have died that week.
It has emerged that Ms Brand has pulled out of an event with the Alzeimer’s society due to take place on Saturday evening.
A statement issued by the society said: “Unfortunately in light of recent events, Jo’s schedule has now changed and she’s not able to attend the Buzz Bingo event, celebrating their contribution to Alzheimer’s Society."
On Friday, Ofcom said they had received 287 complaints about the comments, which the police are also investigating.
Complaints about BBC programmes are initially assessed internally. This process has not been completed yet, given that the incident happened on Tuesday.
The media regulator will only step in if complainants to the BBC are not satisfied with the organisation’s response.
So far, the BBC has taken the clip off its BBC sounds website and issued a statement saying: “Heresy is a long-running comedy programme where, as the title implies and as our listeners know, panellists often say things which are deliberately provocative and go against societal norms but are not intended to be taken seriously.
“We carefully considered the programme before broadcast. It was never intended to encourage or condone violence, and it does not do so, but we have noted the strong reaction to it. Comedy will always push boundaries and will continue to do so, but on this occasion we have decided to edit the programme. We regret any offence we have caused.”
Appearing at an event in Henley, Oxfordshire, on Thursday, the comedian apologised for making a "crass and ill-judged" joke.
But she reportedly told the audience she did not think that she had made a "mistake", adding that she had not mentioned Nigel Farage.
But Mr Farage called her comments “incitement of violence” and said the police must act, although he claimed not to have made a complaint.
He told the Telegraph: “I’m going to ask Jo Brand and the BBC whether they would like to contribute to the costs of keeping me safe,” in a reference to the tens of thousands of pounds a year he spends on security.
“This is way above any norms of free speech - it is appalling and the fact that the BBC spends £177 million a year on light entertainment and comedy… this was a pre-recorded programme which they still chose to put out.”
Eamon Holmes said on his Talkradio show: “I would be taken off air,” if he had made the same comments.
“I like Jo Brand a lot, I think she’s very funny but you just cannot in this day and age, tell people like Katie Piper who was badly disfigured with acid being thrown at her, that it’s funny,” he added.
On Friday night the Metropolitan Police said: "Police received an allegation of incitement to violence on 13 June, relating to comments made on a radio programme. The referral has been considered by the MPS and no further police action will be taken in relation to this allegation."