London mayor Sadiq Khan has called on Londoners to stand together against hate crime following a string of racist and xenophobic incidents over the weekend following the historic Brexit EU referendum vote.

The doors of a Polish community centre in Hammersmith were sprayed with the words 'f*** off', while in Cambridgeshire, police are investigating offensive leaflets that were found on 24 June, one day after the referendum, stating "Leave the EU – no more Polish vermin".

The mayor said in a statement: "As your Mayor, I take seriously my responsibility to defend London's fantastic mix of diversity and tolerance. 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.

"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. While I'm mayor, addressing hate crimes will be a priority for the Met[ropolitan Police]. We will have a zero-tolerance approach to any attempt to hurt and divide our communities.

"It's also crucial that we don't demonise the 1.5 million people in London who voted for Brexit. While I and millions of others disagreed with their decision, they took it for a variety of reasons and this shouldn't be used to accuse them of being xenophobic or racist.

We must respect their decision and work together now to get the best deal for London."

There were also reported of racist abuse shouted at black and ethnic-minority people following the Brexit win, with reports on social media of people being told to leave the country in what some fear are attacks that the perpetrators feel have been legitimised by the referendum vote.

In an interview with Sky News, Baroness Warsi, who quit the Leave campaign prior to the referendum over what she called its "xenophobia", said: "The atmosphere on the street is not good. This is what I said before the campaign, that long after the political bus moves on, we leave problems so our streets.

"So it's important for politicians to come out right now, talk about the vision they have for the country – a united country – and then take that forward for a positive vision of this country which is both stable and secure."

Xenophobic abuse against Polish people reportedly increased so much so over the weekend that it prompted the Polish Embassy in London to issue a statement reassuring people the incidents were being investigated.

The Polish Embassy said in a statement: "We are shocked and deeply concerned by the recent incidents of xenophobic abuse directed against the Polish community and other UK residents of migrant heritage.

"The Polish Embassy is in contact with relevant institutions, and local police and already investigating the two most widely reported cases in Hammersmith, London, and Huntingdon, Cambridgeshire."

"We call on all Polish nationals who fall victim of xenophobic abuse and non all witnesses to report such incidents to local authorities."

Pride 2016
Mayor of London Sadiq Khan, pictured at Pride with his wife Saadiya Khan on 25 June 2016, has urged Londoners to unite Chris J Ratcliffe/Getty