SADIQ Khan, the new mayor of London, has launched an angry attack on Donald Trump, accusing the US presidential hopeful of fuelling extremism with his “ignorant” views on Islam.

The billionaire businessman appeared to seek to extend an olive branch to the Labour politician, when he welcomed his election as the first Muslim mayor of a major European capital.

Asked by the New York Times how his proposed ban on Muslims would apply to Mr Khan, Mr Trump replied: "There will always be exceptions."

But the Republican candidate’s offer was brusquely brushed aside by Mr Khan, who warned that the billionaire businessman's outspoken views on Islam risked endangering people on both sides of the Atlantic.

"Donald Trump's ignorant view of Islam could make both of our countries less safe,” declared Mr Khan, who beat off the challenge of Tory Zac Goldsmith in his fight to get to City Hall.

“It risks alienating mainstream Muslims around the world and plays into the hands of extremists," claimed the mayor, who announced he would be standing down from his Tooting seat thus sparking a parliamentary by-election.

"This isn't just about me,” insisted Mr Khan, “it's about my friends, my family and everyone who comes from a background similar to mine, anywhere in the world."

He added: "Donald Trump and those around him think that Western liberal values are incompatible with mainstream Islam; London has proved him wrong."

Earlier, the London mayor warned that if he wanted to meet his counterparts in New York and Chicago, he would have to go before the presidential inauguration in January in case Mr Trump succeeded in winning the presidency.

"I want to go to America to meet with and engage with American mayors. If Donald Trump becomes the president, I'll be stopped from going there by virtue of my faith, which means I can't engage with American mayors and swap ideas," he told Time magazine.

However, Mr Trump, who has been seeking to soften his image since all but clinching the Republican nomination, insisted that he welcomed Mr Khan's election.

"I was happy to see that. It's a very good thing and I hope he does a very good job because, frankly, that would be very, very good," he said.

The tycoon added: "You lead by example, always lead by example. If he does a good job, and frankly if he does a great job, that would be a terrific thing."

Meantime, George Galloway, the former London, Yorkshire and Scottish MP, said he was “almost certain” to stand in the forthcoming Tooting by-election as an independent.

“My track record shows I’m good at by-elections. Labour’s small majority in Tooting is an indication of the extent of the disappointment in them, dissatisfaction actually.”

Mr Galloway added that he had local links. “I lived next door to Tooting for nearly 20 years until about 18 months ago. Mt GP, even my barber, is still there.”

Labour’s majority in Tooting is 2,842. The timing of the by-election is in the gift of the incumbent party but is likely to be in early July.