'It's up to (lawmakers) to take a stand, I've done so, if others feel that it's right for them to do so then good on them'.
"My brother Boris, who led the leave campaign, is as unhappy with the Government's proposals as I am", he said.
He added: 'This is one of the most momentous questions we will ever face in our political careers.
"And everybody is thinking very hard about it".
Johnson wants a three-way referendum giving the people a choice between remaining in the EU, May's deal and no deal.
While the majority of his constituents voted to leave the European Union, he rejected the idea that a vote on "what an idealised Brexit might offer" versus what was being delivered in reality, matched up to what many had voted for, describing the current state of things as an affront to democracy.More news: Delhi gasps for air as pollution gets ‘severe’
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In an article sent to journalists, the MP for Orpington said he would vote against the withdrawal agreement which the prime minister was trying to agree with the European Union, describing it as "a awful mistake".
Johnson announced on Friday that he was quitting the government because Britain was "barrelling towards an incoherent Brexit" and claimed "what is now being proposed won't be anything like what was promised two years ago". "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.
In marked contrast to his brother, who remains firm that leaving the European Union without a deal would be no bad thing, and resigned because he believed the deal being negotiated was too soft, Mr. Jo Johnson called for a second referendum.
This week, International Trade Secretary Mr Fox openly challenged Mrs May over the Irish border backstop.
Instead, Johnson said it would be proper to give the British public a chance to vote again because of the way the Brexit negotiations have evolved. That needs to be an issue for a sovereign British government to determine'.
The EU insists that a deal must lead to either a soft Brexit for the entire United Kingdom, or a sea border between Great Britain and Northern Ireland.
Quitting as a junior transport minister, Johnson called May's Brexit plans delusional and said he could not vote for the deal she is expected to unveil in parliament within weeks.