There has been an increase in hate crimes and community tensions since last week's referendum.
Initial figures show an increase of 57 per cent in reported incidents between Thursday and Sunday, compared with the same days four weeks earlier, the National Police Chiefs' Council said; 85 incidents were reported compared with 54 during the earlier period.
Racist graffiti was found scrawled across the doors of the Polish Social and Cultural Centre (POSK) in Hammersmith, west London, on Sunday.
In another incident in Huntingdon, Polish origin schoolchildren received cards calling them "vermi" who must "leave the EU."
In Barnsley, a TV correspondent noted that within five minutes three different people had shouted, "Send them home", while a huge banner was unfurled in Newcastle calling for "repatriation" of migrants.
The Muslim Council of Britain has compiled a dossier of reported racist and Islamophobic incidents since the result of the referendum was announced on Friday morning.
In a CNN debate on the issue on Monday, Hannan, an ECR group deputy and one of the leading Leave campaigners, fiercely denied that the rise had anything to do with the Leave campaign.
When it was pointed out that the Leave camp had made migration and immigration central planks of their call for the UK to leave the EU and asked if the incidents were connected to this, Hannan said, "This apparent increase in racist attacks in the UK has nothing to do with our campaign. You will always get people who do these sorts of things."
However, Humza Yousaf, of the Scottish Nationalist Party, hit back saying, "For Hannan to say this is outrageous. He should be ashamed of himself."
Elsewhere, the European Network Against Racism (ENAR) said it was "extremely concerned" by the "numerous" reports of racist speech and attacks aimed at Polish, Muslim and other Black and ethnic minorities in the UK.
It called on UK political leaders to "strongly" respond to and publicly condemn the incidents, as well as prevent a further rise in hate crimes.
Amel Yacef, new ENAR chairman, said, "Xenophobic and racist discourses were part of the campaign in the run-up to the referendum. These latest incidents show that political hate speech can escalate into real life and have a very tangible and destructive effect on minority communities in the UK.
"Police and law enforcement authorities must adequately investigate and prosecute these incidents as hate crimes and ensure the perpetrators are brought to justice.
"UK leaders and politicians must speak out against and challenge hatred and prejudice and the discourses that fuel them. They should ensure hate crimes are addressed. They should also take concrete measures to counter cross-community division and support such initiatives at local level.
"In the current divisive context, political leaders must ensure that all members of society feel worthy of security, protection and wellbeing"
Yacef added: "British society should not give in to revengeful racist nationalism against communities who have steadfastly contributed to the growth and sustainability of the UK economy and society.
"When the backlash of the Brexit vote is likely to hit the UK economy, the last thing the UK society wants is to alienate and divide its communities."