Former Chancellor Philip Hammond has accused the PM of trying to wreck the chance of a new Brexit deal, by making demands the EU could never accept.
In a Times article, Mr Hammond said a no-deal Brexit would be "a betrayal" of the 2016 referendum result.
He told the BBC he was "confident" that Parliament "has the means" to express its opposition to a no-deal exit.
A No 10 source said the UK would leave on 31 October despite Mr Hammond's "best efforts to the contrary".
The source added that Mr Hammond, as chancellor, "did everything he could" to block preparations for leaving and had "undermined negotiations".
The former chancellor rejected this suggestion in a tweet, saying he wanted to deliver Brexit "and voted to do so three times".
Wrong.— Philip Hammond (@PhilipHammondUK) August 13, 2019
I want to deliver Brexit - and voted to do so three times.
But ‘No Deal’ is a far cry from the highly optimistic vision presented by the Leave campaign - and there is no mandate for it. https://t.co/ksfIdtYDXa
Prime Minister Boris Johnson has said he wants to leave the EU with a deal, but the UK must leave "do or die" by the latest Brexit deadline of 31 October.
He wants the EU to ditch the Irish border backstop plan from the deal negotiated by former PM Theresa May, which was rejected three times by Parliament.
But the EU has continued to insist that deal, including the backstop arrangements, is the only agreement possible.
Many of those who voted against the deal had concerns over the backstop, which if implemented, would see Northern Ireland staying aligned to some rules of the EU single market.
It would also see the UK stay in a single customs territory with the EU, and align with current and future EU rules on competition and state aid.
These arrangements would apply unless and until both the EU and UK agreed they were no longer necessary.
Speaking on BBC Radio 4's Today programme, Mr Hammond said a no-deal exit would be "just as much a betrayal of the referendum result as not leaving at all".
He said that Mr Johnson's demand for the backstop to be entirely removed from the deal meant a no-deal was inevitable on the current 31 October deadline.
He said that agreeing to changes now would "fragment" the EU, adding: "they are not going to take that risk".
"Pivoting to say the backstop has to go in its entirety - a huge chunk of the withdrawal agreement just scrapped - is effectively a wrecking tactic," he said.
He also told Today that he was "very confident" MPs would be able to pass legislation to express their opposition to a no-deal exit.
However he said he did not favour the tactic of replacing the PM with a national unity government designed to prevent no deal, saying: "I don't think that's the answer".
'Travesty of the truth'
In his Times article, Mr Hammond said "the unelected people who pull the strings of this government know that this is a demand the EU cannot, and will not, accede to."
BBC political correspondent Tom Barton said that remark was an apparent aim at the prime minister's closest adviser, Dominic Cummings - the former Vote Leave campaign director.
It was a "travesty of the truth", Mr Hammond wrote, to pretend that Leave voters backed a no-deal Brexit in the 2016 referendum.
But Leave-supporting former Tory leader Iain Duncan Smith, also speaking on the Today programme, said he was "astounded" by Mr Hammond's remarks.
"Talk about hubris. This man did nothing to prepare us for leaving with no deal," he said.
"The fact we are now doing that means we have a much better chance to get some kind of agreement from them because they now know we're going to leave with no deal and he's undermining that."
Parliamentary battles ahead
Mr Hammond's comments come as Downing Street said it expected a group of MPs to try to block a no-deal Brexit by attempting to pass legislation when Parliament returns next month.
The Daily Telegraph reports that Commons Speaker John Bercow told an audience at the Edinburgh Fringe festival that he "strongly" believes the House of Commons "must have its way".
He said he would "fight with every breath in my body" any attempt by the prime minister to suspend Parliament to force through a no-deal against MPs' wishes.
On Tuesday, Work and Pensions Secretary Amber Rudd urged Mr Johnson not to force through a suspension.
She told the BBC: "I remain a great admirer of Parliament and of parliamentary sovereignty and I will continue to argue for the executive of the government that I'm part of to work with Parliament, not against them."
Meanwhile, 20 other senior Tory MPs have written to the prime minister to say his demand to scrap the Irish backstop "set the bar so high that there is no realistic probability of a deal being done".
The MPs said they were "alarmed by the 'Red Lines' you have drawn which, on the face of it appear to eliminate the chance of reaching agreement with the EU".
The group also demands that Mr Johnson declares he is firmly committed to leaving the EU with a deal and is ready to compromise to get one - pointing out those were assurances he gave during the leadership campaign "both publicly and privately".
Seven other former cabinet ministers have signed the letter, including David Lidington, David Gauke, Rory Stewart and Greg Clark, all of whom resigned before Mr Johnson took office.