The London mayor, Sadiq Khan, has said he wants London to take over from Los Angeles as one of the film capitals of the world and attract the diverse industry talent who no longer feel welcome in Donald Trump’s America.

Khan, speaking on a visit to a visual effects company, laid out plans for the capital to become the “world’s most film-friendly city”, emphasising that the UK film industry had injected a record £1.35bn into the economy last year.

Khan also addressed the US president’s “cruel and shameful” travel ban on those from seven majority-Muslim countries, and emphasised that while it was still in place “we should not be rolling out the red carpet” for Trump to make a state visit to the UK.

He said that while he believed “America was wrong” to introduce the policy, if those in the film industry no longer felt welcome or comfortable working in America, they should come to the UK.

Khan said: “Film-makers, those involved in this industry, will have seen what Donald trump has said. If it’s the case that Donald Trump’s policies are leading those people to leave America, they are welcome here.”

Khan also warned that despite a “golden decade”, Brexit presented a challenge to London maintaining its position as a global hub for film-making.

“When you speak to people in the film industry, one of the biggest concerns they have is that the government doesn’t appear to understand how diverse our film ecosystem is,” said Khan. The mayor said he had recently met the minister overseeing Brexit, David Davis, to discuss how to protect the film sector.

“The reality is our diverse ecosystem relies upon talent from across the EU. What we can’t afford to happen is those talented people not being able to come to London. When I speak to the government I’m impressing on them the importance of making sure we have access to that talent.”

Khan has set up a study exploring the possibility of building a new 17-acre film studio, to be London’s biggest, in Dagenham, just one of the ways to “catch up with New York and take over LA” in terms of attracting film-makers.

Since the introduction of film tax breaks, franchises from Harry Potter, the Avengers and the new Star Wars films have all been filmed in studios in and around London.

The mayor, speaking at visual effects company Double Negative, also said he was proud of the thousands of protesters who took to the streets of London on Monday night to vocalise their disgust at Trump’s immigration policy and Theresa May’s refusal to rescind the invitation for the president to visit the UK in June, and had high hopes it had made an impact on the government.

“I’m optimistic there won’t be a state visit while the ban is in place. To be seen to be endorsing or condoning the ban is just wrong.”

He said if the visit did take place, he would “make plans to make sure that Londoners have their right to protest and have their voices heard loud and clear”.

“I believe in the real facts rather than alternative facts and I encourage my fellow citizens to make their voices known, peacefully and loudly and clearly,” said Khan.