At the party conference, Labour delegates left open the possibility of backing a second referendum if it could not force a general election.
Amid the Tory infighting, DUP leader Arlene Foster made it clear her party would vote against the PM's current proposals.
"Contrary to promises, there is in fact no deal at all on our future trading relationship with the European Union which the government can present to the country", he wrote.
However, there are concerns that a second referendum could embolden the far-right in the United Kingdom, while Eurosceptics point to examples where votes within EU member states rejecting greater federalism and austerity have been overturned in what they say is yet more evidence that there is a "democrat deficit" within the union.
"To present the nation with a choice between two deeply unattractive outcomes, vassalage and chaos, is a failure of British statecraft on a scale unseen since the Suez crisis", he wrote, adding that from the work of his own Department he was aware that a no-deal scenario could threaten the country's access to fresh food and medicine.
In his resignation statement, Johnson said the withdrawal agreement being discussed by the European Union and British leaders would be a "terrible mistake" that would leave Britain weaker economically and with "no say" in EU rules it must follow, and years of uncertainty for business.
Boris praised Johnson's decision, saying they were "united in dismay" at Prime Minister May's handling of the Brexit negotiations.
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But in a warning to his brother and fellow Brexiteers, he added: "Inflicting such serious economic and political harm on the country will leave an indelible impression of incompetence in the minds of the public".
The better alternative, he believes, is to have another vote on whether the people want to actually leave now when they know the cost they will have to pay.
"Maybe three Johnsons. Dad's joined in as well, I understand".
Rachel said that she felt there had been a "change of mood" in light of her brother's resignation. "It does not remotely correspond to the mandate of the people in June 2016".
"Britain stands on the brink of the greatest crisis since the Second World War".
But calls for a second Brexit referendum have been attacked by ex-first secretary of state Damian Green.
Like his older brother, Mr Johnson enjoyed a distinguished career in journalism before entering politics, working for the Financial Times as, among other roles, South East Asia bureau chief and Paris correspondent.