It comes amid reports of several race-related incidents over the weekend.
"Racist" graffiti was found scrawled on a Polish cultural centre in Hammersmith, west London, the Met said.
London Mayor Sadiq Khan said he had asked Scotland Yard to be "extra vigilant" following the reports.
The Polish ambassador to Britain Witold Sobkow expressed shock at what he called incidents of "xenophobic abuse" directed against the Polish community.
He said: "The Polish Embassy is in contact with relevant institutions and local police are 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 on all witnesses to report such incidents to local authorities."
He also thanked the British public for messages of support and solidarity the Polish community had received.
Police are investigating the vandalism at Hammersmith's Polish community building after images on social media appeared to show offensive graffiti smeared in yellow paint across the entrance. It was later removed.
Cambridgeshire Police are also investigating suspected post-referendum racism after notes were allegedly posted through letterboxes of Polish residents in the county.
Laminated cards reading "leave the EU - no more Polish vermin" were reportedly delivered to members of the Polish community in Huntingdon, north west of Cambridge, on Saturday.
Other incidents were also reported on social media, while a hashtag of #PostRefRacism was being used on Twitter.
Sky News journalist Adam Boulton tweeted: "This weekend I and my family have witnessed 3 "when are you going home?" Racist incidents aimed at EU citizens here."
Another user, James Titcombe, tweeted: "Daughter tells me someone wrote '[Child's name] go back to Romania' on the wall in the girls toilets at School today".
And former Conservative party deputy chairwoman Baroness Warsi also tweeted a string of reports of racist incidents, saying: "This is not the post Brexit Britain we want to see. Politicians from all sides need to speak out "
The Muslim Council of Britain said there had been countless incidents reported in the days since the referendum result as well as shocking manifestations of hate speech both online and also on the streets of Britain.
They included a demonstration outside a Birmingham mosque and reports of Muslims and others being told to "go back home", it said.
It called on political and civic leaders to urgently come together and heal the divisions that had emerged as a result of the referendum campaign.
Dr. Shuja Shafi, secretary general of the Muslim Council of Britain, said: "Now we are witnessing the shocking extent of this with reports around the country of hate speech and minorities being targeted. We need leadership now more than ever before."
Mr Khan echoed those sentiments calling on "all Londoners to pull together and rally behind this great city."
He said: "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."
The Metropolitan Police are on heightened alert for a rise in hate crime following the European referendum result.