It comes as it was revealed that the number of hate crimes reported to police have soared by 57% since the vote for the UK to leave the EU.
Sima Kotecha, a BBC One and Radio 4 journalist, said she was in "utter shock" after being called a "p**i" in her home town - a word she says she has not heard in that area since the 1980s.
Dozens of people responded to Kotecha on social media, condemning the abuse that she received.
Labour MP Paula Sherriff said the abuse was "absolutely shocking", adding that she was aware of similar incidents near her.
Another MP, Alison McGovern, called the abuse "absolutely horrific".
Karen Pollock, chief executive of the Holocaust Educational Trust, said that she was "alarmed and utterly depressed by the number of racist incidents over past few days".
Journalist Anita Anand said that she had heard similar "wretched" stories from friends of hers.
The BBC journalist said she was "touched by the outpouring of support" that she has received and thanked her followers.
This latest incident comes after scores of similar racist encounters were documented online.
Over the weekend a number of people revealed the #PostRefRacism they had received.
Sam Coates, deputy political editor at The Times, said that the racist abuse Kotecha faced in her home town made it "hard to deny link to referendum".
The result of the EU referendum has seen an increase in anti-immigration rhetoric.
A shocking list compiled by Tell MAMA, a group that measures anti-Muslim attacks, details the abuse people, including young children, have received since the vote.
It comes as the National Police Chiefs’ Council reveals that hate crimes reported to the police has risen 57% between Thursday and Sunday compared to the corresponding days four weeks ago.
Faith Matters, an interfaith group that works on countering extremism projects, released the hate crime figures that were reported through Tell MAMA.
Fiyaz Mughal, founder and director of Faith Matters, said that, since Friday’s results, incidents of racist abuse have been reported predominantly from visible Muslim women who have had comments such as “we voted you out, why are you still here” directed at them.
Mughal said: “The Brexit vote seems to have legitimised the prejudice of some people to the point where they are verbalising and targeting people at a street level who are visibly different.
“This is England 2016 and this is totally unacceptable.”
Examples of the racist behaviour documented includes a taxi driver telling a Muslim woman that he voted to leave the EU “to get rid of people like you”.
Other people report being called a “p***” and physical abuse.
Police are investigating suspected racist graffiti scrawled on a Polish community building in London.
Speaking in the House of Commons on Monday, Labour leader Jeremy Corbyn said: "Real concern exists about immigration, but too much of the discussion in the referendum campaign was intemperate and divisive.
"And in the days following the referendum result it appears we have seen a rise in racist incidents such as the attack on the Polish centre in Hammersmith, which the Prime Minister quite rightly referred to, and sadly many such other sad incidents all over this country."
He called for this "disgraceful racist behaviour" to be halted.
Corbyn said that as political leaders it was their "duty" to "calm our language and calm our tone".
David Cameron agreed that "all action" must be taken to "stamp" out intolerance.
SNP MP Angus Robertson also spoke out against the attacks.
Robertson said: "I hope that we all, on all sides, totally repudiate these despicable acts and encourage the police and prosecuting authorities to do all that they can."
Harriet Harman, former deputy leader of the Labour party, said: "The leaders of the Brexit campaign have engendered an atmosphere where some people believe it is open season now for racism and xenophobia.
"Will the Prime Minister say very clearly when it comes to the difficulties of getting a job or problems in the NHS or housing or in schools, that is the responsibility of his government to sort out, not the fault of migrants from the EU or indeed anywhere else."
One man filmed by Channel 4 News in Barnsley admitted that he voted leave “to stop Muslims coming into the EU”.
He said: “It’s all about immigration. It’s not about trade or Europe or anything like that, it’s all about immigration.
“It’s to stop Muslims coming into this country. Simple as that.”
A week before the EU referendum vote, Nigel Farage was lambasted by Ukip's only elected MP for his highly controversial 'breaking point' poster.
Douglas Carswell blasted Farage's “morally wrong” poster, slamming it for using “angry nativism” to try to win the referendum.
The poster was condemned by politicians on both sides of the referendum debate, with Vote Leave’s Michael Gove saying he “shuddered” when he saw the image.