In a letter to all party leaders, the Equality and Human Rights Commission expresses concern about hate attacks that have taken place since the UK voted to leave the EU in June.
It calls for "accurate information and respectful debate" from politicians.
The Home Office said extra money had been allocated to tackle hate crime.
The commission's letter, which is co-signed by its chairman David Isaac and chief executive Rebecca Hilsenrath, said politicians had spoken about "the need to heal the country and bring people together" following the UK's EU referendum.
But instead, it said: "There is growing concern that the divisions on a range of big questions are widening and exacerbating tensions in our society."
It pointed to the killing of Arkadiusz Jozwick, racist, anti-Semitic and homophobic attacks on the streets, and reports of hijabs being pulled off, all of which it described as "stains on our society".
The letter comes after Thomas Mair was jailed for life on Wednesday for the murder of Labour MP Jo Cox during the referendum campaign.
Prosecutors said the attack was "nothing less than acts of terrorism" and the judge said it was carried out to advance a political cause of violent white supremacism.
The commission, an independent statutory body which advises on equality and human rights law, said: "We are concerned that attacks on supporters of both sides of the Brexit debate have polarised many parts of the country.
"There are those who used, and continue to use, public concern about immigration policy and the economy to legitimise hate.
"The vast majority of people who voted to leave the European Union did so because they believe it is best for Britain and not because they are intolerant of others."
It describes the Brexit vote as a "defining moment" for the country, saying that while the focus has been on the economic and trading implications there should also be a "discussion on what values we hold as a country".
The letter also criticises the government's aborted plan to demand companies set out the proportion of foreigners they employ, which was announced by Home Secretary Amber Rudd at the Conservative Party conference in October.
It said "politicians of all sides should be aware of the effect on national mood of their words and policies, even when they are not enacted".
The letter also mentioned the discussion around child migrants, "where dialogue escalated to irrational levels".
And it said there had been an "ambivalent reception" to claims of anti-Semitism in politics, an issue that BBC political correspondent Chris Mason said had dogged the Labour Party in particular.
The commission said it welcomed the government's hate crime plans, but said more concerted action was needed.
It suggested there should be a review of the sentences for hate crimes in England and Wales.
Home Office figures released in October showed racist or religious abuse incidents recorded by police in England and Wales jumped 41% in the month after the UK voted to quit the EU.
The Home Office said there was "absolutely no excuse" for such offences and extra money had been allocated to tackle the issue.
Westminster party leaders should tone down campaigning that has "polarised" the country and "legitimised hate", the equalities watchdog has said.