Politicians and police urged vigilance on Monday after reports of dozens of racist incidents - ranging from demands that people speak English to threats and small protests - following Britain's vote last week to leave the European Union.

Labour's Sadiq Khan - London's first Muslim mayor, elected last month - said he wanted to "defend London's fantastic mix of diversity and tolerance" following a spate of incidents since Thursday's referendum.

"So it's really important we stand guard against any rise in hate crimes or abuse by those who might use last week's referendum as cover to seek to divide us," Khan said in a statement.

"I've asked our police to be extra vigilant for any rise in cases of hate crime, and I'm calling on all Londoners to pull together and rally behind this great city," he said.

The Muslim Council of Britain called for an urgent meeting of political and civic leaders after dozens of "shocking manifestations of hate speech," including: a London Polish centre daubed with racist graffiti; a racist protest outside a mosque in Birmingham; and many reports of "Muslims and others being taunted with 'go back home!' or similar sentiments."

The group compiled social media reports of more than 100 racist incidents since Thursday.

In a statement on Monday, the Polish embassy in London said it was "shocked and deeply concerned by the recent incidents of xenophobic abuse directed against the Polish community and other UK residents of migrant heritage."

US-based Human Rights Watch urged British political leaders - "particularly those who supported the campaign to the leave the EU, which at times included anti-immigrant and anti-refugee rhetoric" - to speak out strongly against racism and xenophobia.

"We need leadership now more than ever before," said Shuja Shafi, head of the Muslim Council, which represents some 2.7 million British Muslims.

"Our country is experiencing a political crisis which, I fear, threatens the social peace," Shafi said.

"Whatever differences we may have, it is vitally important that we demonstrate solidarity for those attacked, and state, in the words of the murdered MP Jo Cox, that we have far more in common than which divides us," he said.

Speaking in parliament, Prime Minister David Cameron said the government "will not stand for hate crime" and promised the authorities will "take every step we can" to protect the targets of racism.

Two people were arrested during a protest by the far-right English Defence League outside the mosque in Birmingham's Sheldon district on Saturday. One man was charged with "racially aggravated public order," threatening behaviour and obstructing police, West Midlands Police said on Monday.

London's Metropolitan Police said it is investigating "offensive graffiti" daubed on the front of a Polish social and cultural centre in London's Ravenscourt Park area on Sunday.

"This incident is being treated as a hate crime due to the racially aggravated nature of the criminal damage," the force said in a statement.

"High visibility foot patrols have been stepped up in the area and we are doing everything to reassure [the Polish community] and other local community groups... that we will deal with any allegations of hate crime robustly and efficiently," local police officer Jenny Doe said in a statement.

In Huntingdon, in the eastern English county of Cambridgeshire, printed cards were distributed at several sites including outside primary schools, reading "Leave the EU. No more Polish vermin" in English and Polish, according to reports and photographs by local media.

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