In a message to warring MPs, the ex-cabinet minister said Theresa May’s Brexit deal was a “threat to the Conservative Party’s very future” and a public vote was the only way to break the impasse in parliament.
The prime minister has repeatedly dismissed calls for a second referendum, as she argued that it could not be held before the official exit day on 29 March.
But Ms Greening said a referendum could easily be held within six months, which would result in a short delay to the Brexit process to allow the government to enact the result of the new vote.
Speaking at an event in London, the pro-EU MP said: “We can have the work done in just a few months. I’ve worked out that you could plan and hold a referendum in 22 weeks.
“My calculations show that we could get through the work of passing legislation, we could get through the work of the Electoral Commission working out the right question... we could do that in 22 weeks.
“We could actually, after this vote on 11 December, hold a referendum, potentially, on 30 May next year.
“We could, alongside that, choose to extend Article 50, I’ve suggested, by four months to 29 July.”
The EU has been clear that “if Britain needs a few more months to resolve the route forward, we would be able to have that”, she said.
Ms Greening said it was not “heresy” to delay Brexit, adding: “Given this decision is going to shape the coming decades, I think we owe it to ourselves and to future generations to get it right.”
Her comments came at a People’s Vote event, where former Tory ministers Jo Johnson and Lord Willetts spoke in favour of the “Conservative case” for a new referendum.
Mr Johnson, who resigned in protest at Ms May’s Brexit plans, warned that the Tories could lose all credibility if they pursue the prime minister’s plan, and clear the way for a Labour victory at the next election.
He said: “Brexit is seen as a project driven by the Conservative Party and this half-baked worst of all words Brexit could trigger an electoral defeat on the scale of 1997 or worse, this ‘Tory Brexit’ label will be an albatross around our necks for years to come.”
Mr Johnson said he even agreed with Brexiteers such as Jacob Rees-Mogg, and his own brother Boris Johnson, that the prime minister’s plan would leave the UK as a “passive recipient” of EU policy.
It comes after EU leaders endorsed the prime minister’s blueprint at the weekend, clearing the way for a Commons showdown on 11 December, where scores of Tory MPs are expected to vote down the deal.
With Labour and the other opposition parties also opposed, shadow chancellor John McDonnell gave his strongest hint yet that Labour would back a second referendum, saying it could be “inevitable” unless there is a general election.
However Ms May told a committee of senior MPs on Thursday that seeking an extension to the withdrawal process would cause the agreement would fall apart.
“Any second referendum that would be held, if that were the case, would not be able to be held by 29 March next year. You would have to extend Article 50,” she told the Commons Liaison Committee.
“What is clear is that any extension to Article 50 – anything like that – reopens the negotiations, reopens the deal. At that point, frankly, the deal can go in any direction.
“We would simply find ourselves in a period of more uncertainty, more division in this country.”
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