Both the Conservatives and Labour have ruled out any second referendum.
Mr Johnson addressed the remarks made by Sir Patrick, who played the role of Captin Jean-Luc Picard in Star Trek: The Next Generation.
Several pro-EU organisations have joined forces to mount an attack on the government's Brexit plans with more than 350 events across the country, ahead of the launch of a £1m campaign demanding the opportunity to stay in the European Union if the people want to.
Andrew put it to Dominic that "there would be more uncertainty, would there not, if we now offer a people's vote" but his response suggested the only uncertainty would be "for the duration of the vote".
Open Britain chief James McGrory said Brexit was "not inevitable".
MPs have been promised a "meaningful vote" on the final deal after inflicted a humiliating parliamentary defeat on the government.
The British parliament's only Green MP, Caroline Lucas, said: "This is too big and too important to be determined exclusively by politicians".
"Brexit will affect everybody in the country, which is why it should not be left to 650 politicians to decide our future but 65 million people".
He also said he was motivated by "history and emotion" to want to stay in the EU.
However, foreign secretary Boris Johnson shrugged off the campaign, insisting that the people have already spoken on Brexit.
Actor Stewart said in a media interview Sunday that if people voted to reject the exit deal, Britain would simply stay in the EU.
Foreign Secretary Boris Johnson countered with a Star Trek allusion of his own, promising that Britain's departure from the European Union will allow it "to boldly go again to areas that perhaps we've neglected over the last 45 years".
Asked what he would say to people who voted for Brexit, he told the programme "what we are doing is in their benefit".
"The idea that uncertainty is going to disappear next year is quite wrong".
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