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 said Parliament would "make its voice heard", adding that a no deal "must not happen".
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".
Prime Minister Boris Johnson has called for the EU to remove the Irish border backstop plan before the Brexit deadline of 31 October.
Many of those who voted against Theresa May's Brexit deal had concerns over the backstop - designed to guarantee there will not be a hard Irish border after Brexit - which, if implemented, would see Northern Ireland staying aligned to some rules of the EU single market.
Mr Hammond, in his first comments since stepping down last month, said the early signs that Mr Johnson could take the UK out of the EU with a deal in place were "not encouraging".
He wrote: "The pivot from demanding changes to the backstop to demanding its total removal is a pivot from a tough negotiating stance to a wrecking one.
"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.