In a furious attack, Ms Greening said the Prime Minister’s Chequers deal was “untenable” and “less popular than the poll tax”.
She told the BBC Radio 4: “Chequers is now dead. There’s no point having a Government spending two vital months working on that.
“What it needs to do is start working on an alternative route for us.”
Her comments came as ex-Foreign Secretary Boris Johnson said Mrs May’s Brexit strategy was a “fix” that can only lead to victory for the EU.
He said: “The UK has agreed to hand over £40 billion of taxpayers’ money for two-thirds of diddly squat.
“We will remain in the EU taxi, but this time locked in the boot, with absolutely no say on the destination.
“We won’t have taken back control, we will have lost control.”
But a Downing Street spokesman delivered a stinging slapdown to Mr Johnson, saying he has produced “no new ideas” on Brexit.
He told reporters: “Boris Johnson resigned over Chequers. What we need at this time is serious leadership with a serious plan.
“And that’s exactly what the country has with this Prime Minister and this Brexit plan.”
Follow the latest Brexit updates below with Express.co.uk’s live blog…
8:52pm: Farage’s shock warning to Johnson
Brexiteer Nigel Farage has warned Boris Johnson not to attempt to launch a Tory leadership coup against Theresa May.
Speaking on his LBC radio show, ex-Ukip leader Mr Farage claimed Mr Johnson “clearly” wanted to become Prime Minister.
But he warned any leadership contest could derail “crucial” Brexit talks and potentially delay Britain’s exit from the bloc.
He said: “I think Boris needs to go further. My main criticism is he is clearly going for the Tory party leadership.
“If Boris brings down Theresa May, it could be difficult to meet the deadline date of Article 50, March 29 2019.”
7:41pm update: Ukip lashes out at Johnson over Brexit comments
Ukip leader Gerard Batten has said Boris Johnson is “finally catching up with Ukip” by attacking Theresa May’s Brexit plan.
Mr Batten said: “We’ve been saying since the very beginning of the process that Theresa May is a committed Remainer.
“Make no mistake, the Tories never had any intention of getting us out of the EU.
“Johnson must bear his own responsibility – he was involved in setting up the initial negotiating strategy when he was Foreign Secretary.
“Perhaps if he wasn’t so loyal to the Tories and put his country first, he would have made these statements much sooner.”
7:18pm update: Irish party to campaign for ‘Irexit’
A new Irish political party will campaign for the Republic of Ireland to leave the European Union.
The Irexit Freedom party, which is set to be launched in Dublin next Saturday, wants Ireland to “take back control” from Brussels.
The party, which plans to run candidates in next year’s European Parliament elections and the 2021 Irish general election.
The group’s spokesman Hermann Kelly is a close ally of former Ukip leader Nigel Farage.
Mr Kelly praised British voters for voting to “take back control of their money, their law and their borders” in the Brexit referendum.
6:46pm update: SNP raises fears over no-deal Brexit
The Scottish Government has highlighted “serious concerns” over the possibility of a no-deal in a letter to Theresa May’s effective deputy.
Writing to David Lidington, Scotland’s Constitutional Relations Secretary Mike Russell said such an outcome would be “irresponsible”.
Mr Russell told Cabinet Office minster Mr Lidington that a no-deal would spark “significant negative economic and social consequences”.
Mr Russell wrote: “As I set out to the Scottish Parliament in June, the Scottish Government needs to prepare for all exit possibilities.
“However, we have serious concerns that a no deal outcome will magnify massively the uncertainties over Brexit.”
5.32pm update: Traders scared by talk of Brexit ‘contingency plans’
Firms which announce ‘hard Brexit’ contingency plans could scare traders and devalue their stock, analysts have warned.
The warning came after Dechra Pharmaceutical, a veterinary products group, saw shares fall by 21.4 percent in the biggest move of the day.
The Cheshire-based firm had published its full-year results and announced it was implementing a “hard Brexit” mitigation plan.
AJ Bell investment director Russ Mould said: “What may be concerning the market are references to contingency plans for a ‘hard Brexit’.”
4.36pm update: Rees-Mogg attacks May’s Chequers plan
Jacob Rees-Mogg, leader of the influential European Research Group of Tory MPs, has attacked the Government’s Chequers plan.
Mr Rees-Mogg told Sky News there were “hundreds of suggestions” for the basis of a deal with the European Union.
He said: “It’s a question of choosing which of the many is the best. It is certainly not Chequers.”
The outspoken Eurosceptic MP made the comments during a visit to Brussels with the House of Commons’ Brexit Committee.
4.01pm update: Pound plunges against euro over Brexit fears
Sterling is set for its biggest daily drop against the euro in more than three months amid growing fears over Brexit.
Traders bought sterling last week after the EU’s chief Brexit negotiator, Michel Barnier, signalled his willingness to strike an exit deal.
But the currency plunged against the euro today after Mr Barnier said he was “strongly opposed” to the Chequers proposal.
In a note, UBS strategists said the “potential ‘cliff’ of a hard Brexit has come more clearly into focus” as negotiations continue.
Neil Jones from Mizuho Bank added: “Weak economic data and bearish political background means this is a double-pronged attack on sterling.”