Johnson - who had backed staying in the European Union in the 2016 referendum - is the younger brother of Boris Johnson, who spearheaded the pro-Brexit campaign and quit as foreign secretary in July over May's Brexit blueprint. His resignation raises fears that other Remainers will follow suit or be emboldened to vote down a deal.
"We may or may not be able to get an agreement in which case we would have to leave the European Union without one, but we're not going to be bounced into having another referendum", he said.
The shadow foreign secretary reiterated that Labour would not back Theresa May's deal unless it passed the party's six tests, underlining once again how the challenge of getting her Brexit agreement through parliament - including past her own backbenchers - could be May's biggest of all.
The minister said that Britain would not accept separate treatment for Northern Ireland under a Brexit deal, and dismissed calls for a second referendum.
"The "new" idea of a United Kingdom customs arrangement does not appear to be a genuinely UK-wide offer but a GB offer and an NI offer badged as one - Northern Ireland in THE EU customs territory and GB in A customs union".
He already expressed fears that the current "chaotic" Withdrawal Agreement being finalised would be "a bad mistake" in a blog, published yesterday to coincide with his departure.
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Rachel's comments on the state of Brexit were subsequently echoed by her father Stanley Johnson who said that the negotiations were "careering into the jaws of death".
"The prime minister thanks Jo Johnson for his work in government".
"This would not be about re-running the 2016 referendum, but about asking people whether they want to go ahead with Brexit now that we know the deal that is actually available to us".
Corbyn angered Labour MPs and supporters when he said Brexit could not be halted in an interview with German newspaper Der Spiegel on Friday in which he also urged the entire country to recognise why people voted to leave.
She said: "Huge respect for Jo Johnson".
The MP, who voted to remain is Boris Johnson's brother - a leading Brexiteer - and argued Britain was "on the brink of the greatest crisis" since World War Two.
An EU diplomat told Reuters earlier on Saturday that they were cautiously hopeful that an EU summit could happen in November to endorse the deal but that the volatile situation in Britain made it very hard to predict.