The vote to leave the European Union was influenced by a fantasy set of promises that have been shown as undeliverable, Jo Johnson has said, as he sought to explain his reasons for resigning from the government on Friday.

The former transport minister accused the Brexit campaign – which was led, in part, by his brother Boris – of offering the public “a false prospectus” that bears little resemblance to the reality of the deal that the prime minister is to present to parliament.

He said it would be a democratic travesty not to go back to the people for another vote.

Johnson suggested that other senior Conservatives might be considering their positions, saying that “many are reflecting hard about the deal that’s looming and how they will respond to it”.

“In the campaign there were undoubtedly promises made that were shown to be undeliverable – no one can dispute that,” Johnson said, pointing to the vision of a low-tax, pro-business, Singapore-style economy on the edge of Europe.

“It was a false prospectus, it was a fantasy set of promises that have been shown up for what they were,” he told the Today programme on Radio 4. “We are now faced with the reality of that in the form of the deal that the prime minister is about to bring back before parliament.

“My view is that this is so different from what was billed that it would be an absolute travesty if we don’t go back to the people and ask if they want to exit the EU on this extraordinarily hopeless basis.”

Johnson, the MP for Orpington in Kent, spoke the morning after announcing his resignation from the cabinet with an open letter that delivered a stinging criticism of the deal negotiated between Theresa May and EU leaders in Brussels. He accused the PM of offering a choice between “vassalage and chaos” and called for a second referendum now that the reality of Brexit had become clearer.

But he denied that his resignation was an attempt to undermine May’s position. “My priority is really just to do my best as a now backbench MP to try and encourage the country to pause and reflect before we do something that is irrevocably stupid,” Johnson said.

“I think it would be a democratic travesty if we didn’t go back to the people and seek to consent for the departure of the EU on that basis.”

Johnson’s move drew criticism from Tory loyalists. Damian Green, the former first secretary of state, said a new referendum would be unlikely to deliver a clear result. He said: “I think a second referendum would be divisive, but it wouldn’t be decisive. All the evidence is that the country is still, more or less, split down the middle.”

• This article was amended on 11 November 2018. Jo Johnson resigned from the government. He was not a member of the cabinet.