The Met Police is appealing for information after several statues in Parliament Square, including one of women's votes campaigner Dame Millicent Fawcett, were vandalised during a protest on Saturday.
Transgender campaigners gathered in front of Parliament to protest against the ruling by the Supreme Court on Wednesday that biological sex defines a woman for the purposes of the Equality Act.
The Metropolitan Police said seven statues were damaged and they are investigating the incidents as criminal damage. No arrests have been made.
A statue of former South African prime minister Jan Smuts was graffitied with the words "trans rights are human rights".
The Met said its officers were in the area policing Parliament Square "but did not witness the criminal damage take place as the area was densely populated with thousands of protestors and it was not reported at the time".
It confirmed it is investigating the graffiti as criminal damage and has asked anyone with information, footage or pictures to come forward.
The Greater London Authority plans to remove the graffiti but this requires specialist equipment and "we are confident this will be done shortly,", the Met added.
On Wednesday the Supreme Court ruled that transgender women with a gender recognition certificate can be excluded from single-sex spaces if "proportionate".
The judges unanimously ruled that the terms woman and sex in the 2010 Equality Act "refer to a biological woman and biological sex" rather than "certificated sex".
Protests against the ruling also took place on Saturday in Reading, Edinburgh and Glasgow.
Ch Supt Stuart Bell, who was leading the policing operation for the protest, said: "It is very disappointing to see damage to seven statues and property in the vicinity of the protest today.
"We support the public's right to protest but criminality like this is completely unacceptable."
The Met confirmed it is also dealing with a number of complaints from the public about signs and images shared on social media that were reportedly displayed at the protest yesterday and "action will be taken if there are signs displayed that breach of the law".
The statue of Dame Millicent Fawcett by artist Gillian Wearing is the only statue of a woman in Parliament Square, where others honoured include international statesmen like Nelson Mandela and Mahatma Gandhi, and former prime ministers Sir Winston Churchill and David Lloyd-George.
Unveiled in 2018, it is also the only statue by a female artist in the square, and was erected following a campaign and petition by the feminist activist Caroline Criado Perez.
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