The mayor of London, Sadiq Khan, has 24-hour police protection after repeated threats on social media.

Khan, who was MP for Tooting before defeating Zac Goldsmith to succeed Boris Johnson as mayor, said levels of abuse had risen since the 2016 EU referendum.

In a three-month period last year, City Hall referred 17 cases to the police and 237 threats were made on social media, the Times reported.

Khan said the abuse had gone from “name-calling, trolling and threats to terrorism”.

He said: “I will not be cowed or bullied by these people, but you can’t escape the fact that those close to me are worried. It can’t be right that one of the consequences of me being the mayor of London and a Muslim in public life is that I have police protection.

“The referendum campaign allowed things to come to the surface and normalised things that should not be normalised.”

Dozens of MPs have said the Brexit crisis has led to them regularly receiving death and rape threats via social media.

On Tuesday, West Midlands police said they were investigating comments by Carl Benjamin, Ukip’s candidate in the European elections, speculating about whether he would rape the MP Jess Phillips.

Security for MPs was boosted after the murder of the Labour MP Jo Cox in the run-up to the 2016 EU referendum.

Khan said there had been a rise in Islamophobia, antisemitism and homophobia, but that he did not place the blame at the door of leavers.

However, he said: “It starts with name-calling, it can lead to criminal damage and graffiti [and] ultimately to the situation where Jo Cox is murdered or a terrorist can come to London and try to divide communities.”