The U.S. president and May were meeting British and American business leaders on the second day of Trump's state visit to Britain.
"Let's do this deal", Trump said.
"I think Donald Trump is clearly out of his mind, if he thinks that's a sensible way to proceed - you can't ban people going to the United States in that way, or indeed to any country", Johnson said in the video projected on the base of Big Ben by anti-Brexit activists.More news: Bangladesh start World Cup with South Africa win
Trump thanked May for doing a fantastic job and said he didn't know May's timings but that she should stick around. It repeated the phrases "No collusion", "You are fake news", and "I'm a very stable genius" - the audio of which is Trump's own voice.
President Donald Trump met with Prime Minister Theresa May at 10 Downing Street.
The London Mayor said the United Kingdom should have a "working relationship" with allies, but without the state banquet. The meeting, which had been expected to be a wide-ranging discussion taking in the UK's awarding of 5G infrastructure projects to Chinese tech giant Huawei amid a Washington-Beijing trade war, had been downgraded in recent days following May's announcement of her resignation.More news: Deal or no deal, Britain leaves European Union on Oct 31: Johnson
"It's demonstrated the failure of leadership from our government".
He said he had refused to meet opposition Labour Party leader Jeremy Corbyn, a veteran socialist who criticized Trump at a protest in central London on Tuesday.More news: Higa maintains lead as second round wraps up
On Monday, several visual protests were staged as the president touched down on British soil.