Claire from Sidcup was livid at her comments and demanded the BBC take action over the show.
The BBC had originally defended its decision to not edit Brand's joke.
Her remarks have been widely criticised, with Nigel Farage accusing Brand of inciting violence.
'How can they sack me?'
Speaking outside her £1.9million detached home in Dulwich, south-east London, Brand refused to say sorry, and laughed as she was driven away in a auto.
As she arrived to give a talk in Henley, Oxfordshire, today, Brand was asked her about the chorus of calls demanding that the BBC sack her.
'The allegation relates to comments made on a radio programme.
Her comments were immediately condemned by Brexit Party leader Nigel Farage - who has perviously been doused in milkshake while on the campaign trail - was quick to condemn her.
"Milkshaking" has emerged as a new trend among left-wing activists, who have taken to tossing the drinks at right-wing politicians such as Tommy Robinson, Nigel Farage, Carl Benjamin, and members of the UK Independence Party (UKIP) and Brexit Party. "I believe that is exactly what Jo Brand did on that programme". "I'm not going to do it, it's purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry".
Coren Mitchell said at the end of the show that she hoped Brand's comments had not caused offence, adding that the series had been established to "test the boundaries of what it's OK to say and not say".
The Met said in a statement: "Police have received an allegation of incitement to violence that was reported to the MPS on 13 June".
"What we don't believe in - what I don't believe you or I have ever done - is incited violence and that is the limit to free speech". Especially when it comes to jokes'.
The prime minister's spokesman said Mrs May has been clear that politicians should be able to go about their work and campaign without harassment, intimidation or abuse.
"I note that Brendan Cox has said that violence and intimidation should not be normalised and we should consistently stand against it. The Prime Minister shares this view".
Heresy is a pre-recorded show and the BBC last night acknowledged its content had been reviewed and considered by the BBC before broadcast.
Piers Morgan has accused the BBC of double standards for backing Jo Brand despite firing Danny Baker.
Broadcasting watchdog Ofcom said it has received 65 complaints about the episode of Heresy.
In response to calls to dump the comic, a BBC spokesman said: "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 meant to be taken seriously".