The UK needs to “pause and reflect” before doing something “irrevocably stupid” over Brexit, Jo Johnson said a day after quitting as a minister.
On BBC Radio 4’s Today he called again for another referendum, saying what was being offered fell “spectacularly short” of what had been promised.
The ex-transport minister said it would be a “democratic travesty” to not have another vote.
He denied his actions amounted to a coup against the prime minister.
Mr Johnson, who voted to remain in the EU in the 2016 referendum, stood down as Theresa May’s prospective deal with Brussels was being presented to Cabinet ministers.
Mr Johnson warned the UK faced a choice between “vassalage” under her proposals and “chaos” if it left the EU without a deal.
The MP for Orpington in Kent said he had “happily taken the decision” to end his own ministerial career and, when asked if he thought other ministers would resign, he said if they thought it was right thing for them to take a stand then “good on them”.
Cabinet ministers have been invited this week to read the UK’s draft withdrawal deal with the EU. Theresa May has said the withdrawal deal is 95% done – but there is no agreement yet on how to guarantee no hard border in Northern Ireland.
Downing Street has insisted there will not be another referendum “under any circumstances”.
Mr Johnson told Today: “My view is that this is so different from what was billed that it would be an absolute travesty if we do not go back to the people and ask them if they actually do want to exit the EU on this extraordinarily hopeless basis.”
Asked if his brother had lied to voters during the referendum, he said: “In the campaign there were undoubtedly promises made that have shown to be undeliverable. No one can dispute that.”
He added: “It was a false prospectus. It was a fantasy set of promises that have been shown up for what they were. We are now faced with the reality of that in the form of a deal the prime minister is about to bring back before parliament.”
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He added he had become “deeply concerned” about the potential impact of a no-deal outcome while a minister.
His call for another vote was attacked by the Conservative MP and leading Brexiteer, Jacob Rees-Mogg, and the former First Secretary of State Damian Green.
Mr Green told Today another referendum “would be divisive but it wouldn’t be decisive”, and all the evidence showed the country was “still, more or less, split down the middle”.
Mr Rees-Mogg said Mr Johnson was “re-heating ‘Project Fear’ to stop us leaving”.
For Labour, Shadow Brexit Minister Jenny Chapman said the resignation meant Mrs May had “lost all authority and is incapable of negotiating a Brexit deal within her own party, let alone with the EU”.
But asked in an interview with the German magazine Der Spiegel whether he would stop Brexit if he had the chance, Labour leader Jeremy Corbyn replied: “We can’t stop it, the referendum took place.”
Mr Johnson is the sixth minister in Theresa May’s government to resign specifically over Brexit, following David Davis, Boris Johnson, Philip Lee, Steve Baker and Guto Bebb.
Analysis by BBC political editor Laura Kuenssberg
For some time, Jo Johnson has struggled with the unfolding reality of Brexit.
A well-respected and liked member of the government, he has decided that what was promised to people during the referendum campaign is now so different to what is on the table that he has quit the government instead.
He’s not the first, nor the best-known minister to resign over Brexit. But to leave at this moment, right when Theresa May is trying to stitch together a final deal, could have a serious impact.