Theresa May had earlier dodged repeated questioning about President Trump's tweets, declining to criticise the president and instead opting to praise Mr Khan and their close working relationship following the attacks.
Mrs May had faced calls to distance herself Mr Trump for his incendiary remarks but for two days failed to directly address them.
"Our special relationship with the USA means that we will stand up and speak out when something is wrong, and Donald Trump is wrong about many things. I'm not tangoing with this guy, I've got better things to do", said Mr Khan.
Donald Trump Jr. joined his father in criticizing London Mayor Sadiq Khan in an interview that aired Tuesday on ABC. "MSM is working hard to sell it!", Trump said in a Tweet.
Of course, famous Londoner and known Trump critic J.K. Rowling had something to say about the situation, writing on Twitter on Tuesday, "I'd rather he [Trump] didn't come, but if he does, I'd like his vile Tweets juxtaposed against whatever he's been coaxed to read off an autocue".
German minister sees hope of 'soft' Brexit, with conditions
In recent days European Union officials have met Olly Robbins , the permanent secretary of the Department for Exiting the EU. The UK would seek a softer break from the EU, Rasmussen added.
Trump has previously clashed with Khan, who is one of the West's most prominent Muslim politicians. Khan was among those protesting the visit, saying at the time that Trump's immigration ban was "cruel". May answered "yes", when asked if Trump's visit will go ahead, the newspaper reported.
Trump criticises London Mayor.
The president kept up his attacks on Khan the next day. "And there are many things about which Donald Trump is wrong", he added.
President Trump fired off a series of critical tweets over Mr Khan's handling of the London Bridge terror attack, mocking the mayor's comments that there was "no reason to be alarmed" over armed police on the streets. "We have constant attacks going on, not just there but across the globe, and we have to start putting national security and global security at an all time high", she told a White House briefing.
Khan, a human rights lawyer and practicing Muslim hails from Pakistan, has challenged repeatedly Trump's calls to ban Muslims or people from Muslim countries from entering the U.S, saying the president has a "rude view of Islam". Khan was talking about a bombing in NY and said it was essential that cities would be prepared for such cases.