Asked to guarantee he would not walk out – if his senior colleagues decide to keep close alignment with EU regulations in a long-term trade deal – the Foreign Secretary ducked the question.
Instead, he said only: “We are all very lucky to serve and I’m certainly one of those.”
The comment came at the end of a major speech in which Mr Johnson said it would be “intolerable and undemocratic” if Britain had to follow EU laws over which it had no say.
The stance is a direct challenge to Theresa May, ahead of the “away day” next week at which the Cabinet is meant to agree to a united policy on whether to keep close ties with the EU, or make a clean break.
However, Mr Johnson insisted he remained fully behind the Prime Minister’s aims for withdrawal. Asked if she was the “cure” for the country’s Brexit divisions, he replied: “Yes.”
The speech – which did not set out any new detailed Brexit policy – was criticised immediately by one prominent Conservative MP, Sarah Wollaston, the chair of the Commons Health Select Committee.
Ms Wollaston said she hoped Mr Johnson was “right” to be optimistic about Brexit, but tweeted: “His speech did not address any of the serious practical difficulties that will affect real people’s lives with a hard #Brexit.”
And there was an immediate backlash from Brussels to the Foreign Secretary’s claim that Britain was being held back by the EU’s determination to “build a united states of Europe”.
Brexit talks: Top issues facing UK on leaving EU
Jean-Claude Juncker, the European Commission president, said it was “total nonsense” to suggest the aim was a “European super state”.
Lord Adonis, the former Labour cabinet minister and supporter of the pro-EU Best for Britain campaign, attacked Mr Johnson’s refusal to say whether he would resign as “more juvenile game playing”.
In contrast, the Leave Means Leave campaign hailed the speech as an “optimistic vision of Brexit”.
“This is the positive tone the British public have been waiting for the Government to deliver,” said a delighted Richard Tice, the organisation’s co-chair.
The 31-minute speech was billed as an attempt to build bridges with Remain voters who, he admitted, feared Brexit would make them less prosperous, less secure and cut off from Europe.
Mr Johnson urged Britain to have confidence in its “amazing economy”, adding: “We are the nation that has moved the furthest up the value chain of the 21st century economy.
“We are a nation of inventors, designers, scientists, architects, lawyers, insurers, water slide testers, toblerone cabinet makers.”
Any decision to remain aligned to the EU in some areas must be “voluntary”, not laid down in a post-Brexit trading treaty, Mr Johnson said.
The Foreign Secretary insisted the Brexit vote had been one for a positive future, denying it was “some un-British spasm of bad manners” and adding: “It’s not some great V-sign from the cliffs of Dover.”
And on the campaign for a further referendum on the final Brexit deal, Mr Johnson said: “I believe that we would simply have another year of wrangling and turmoil and feuding in which the whole country would be the loser.”