Theresa May’s official spokesman told reporters that Mr Johnson had “no new ideas” and said the country needed “serious leadership with a serious plan” as a battle against a widely expected leadership challenge erupted.
The open warfare among Conservatives comes less than a month before the party’s conference and threatens to destabilise the government further in the middle of a critical phase in Brexit talks.
Mr Johnson used his regular Daily Telegraph column to brand the Prime Minister’s Chequers plan that saw him resign from government a “fix” that can only lead to victory for the EU.
He claimed the UK was “lying flat on the canvas” in withdrawal talks by offering to align UK standards on goods to the EU.
Mr Johnson accused “some members” of the Government of deliberately using the Irish border question to “stop a proper Brexit” and effectively keep Britain in the EU.
He said that the real “scandal” was “not that we have failed, but that we have not even tried” on Brexit.
“The UK has agreed to hand over £40 billion of taxpayers’ money for two-thirds of diddly squat,” he said.
Under the Chequers plan, “we will remain in the EU taxi, but this time locked in the boot, with absolutely no say on the destination”.
But Mrs May’s spokesman insisted that the plans set out in the Government’s Brexit White Paper were “the only credible and negotiable plan which has been put forward”.
He added: “Boris Johnson resigned over Chequers. There’s no new ideas in this article to respond to.
“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.”
Mr Johnson’s intervention won the backing of leading Tory Brexiteers Steve Baker, who described it as “superb” and Owen Patterson, who said it offered a clear articulation of the “myths” surrounding the Irish border.
And in a further sign of the challenge facing Mrs May as she tries to get a Brexit agreement through parliament, the Remain-supporting former cabinet minister Justine Greening said the Chequers plan was “now more unpopular than the poll tax.”
Ms Greening said the deal was “untenable” with only 15% support from the public.
“Chequers is now dead and there’s no point having a government spending two vital months working on that when what it needs to do is start working on an alternative route for us,” she said.
Jacob Rees-Mogg, in Brussels for the Brexit Select Committee’s meeting with EU chief negotiator Michel Barnier, said the Chequers plan was “certainly not” the best way forward.
Mr Rees-Mogg, the leader of the influential European Research Group of Tory MPs, said there were “hundreds of suggestions” that were better than Chequers.
Other leading Conservatives rallied to the Prime Minister’s aid, with Home Secretary Sajid Javid insisting Tories should unite behind Mrs May’s blueprint.
“For those who think there is a different way then they need to properly set out what alternatives there might be,” Mr Javid said.
His predecessor as Home Secretary, Amber Rudd dismissed Mr Johnson’s attack as “ridiculous”.
“This isn’t a strategy, it is not a plan,” Ms Rudd told the BBC. “Once again it is a case of leap before you look.”
The former Brexit Secretary, David Davis also sought to shore up Mrs May’s position, telling ITV that she should not be replaced at the helm of the party. In an apparent attack on Mr Johnson, Mr Davis said it was not the time for “personality politics”.
Asked if it would be better if Mrs May stood down, Mr Davis said: “No, we don’t need any more turbulence right now.
“What matters in all of this is not the personality politics, it’s the outcome at the end.”
Labour leader Jeremy Corbyn said: “It sounds like it is and it sounds like Boris Johnson, having spent two years as Foreign Secretary, has achieved nothing and now says it’s all off.
“Well surely, it’s time for some serious people to take over the negotiations? The Tories have had two years since the referendum and made no progress at all.”