In an article for The Mail on Sunday, Theresa May warns rebels on both sides of her party that there is no other "workable alternative future trading relationship" to the plan agreed at Chequers, and fleshed out in a white paper this week.
However, former Brexit secretary David Davis, who quit in protest at the prime minister's proposals, blasted an "astonishingly dishonest" claim there is no substitute plan for leaving the EU.
His criticism was followed up by a direct attack on the "oddly secretive" Mrs May by influential Tory Brexiteer Jacob Rees-Mogg.
The prime minister's intervention follows demands from Brexiteers that she change her approach, or face a leadership challenge.
Hitting back at accusations made by critics, including Mr Davis and former foreign secretary Boris Johnson, Mrs May insists her proposed solution would restore national sovereignty, end the payment of "vast membership subscriptions" to Brussels, allow for an independent trade policy and create a new economic and security partnership with the EU.
Mrs May wrote: "This is the scale of the opportunity before us and my message to the country this weekend is simple: we need to keep our eyes on the prize. If we don't, we risk ending up with no Brexit at all.
"This is a time to be practical and pragmatic - backing our plan to get Britain out of the European Union on 29 March next year and delivering for the British people."
Mrs May also turned her focus to a crucial vote in the House of Commons on Monday, in which both europhile and eurosceptic Conservative MPs could rebel against the government's trade bill, a key piece of Brexit legislation.
She wrote: "There are some planning to vote for amendments that would tie us to a permanent customs union with the EU. This would be the ultimate betrayal of the Brexit vote.
"It would remove our ability to have an independent trade policy at all, conceding Britain's role on the global stage as a force for free trade and endangering people's jobs and livelihoods. This government will never stand for that."
"There are others who are planning to try and bring down a bill that is essential in enabling us to prepare for life outside the European Union. This would put at risk our ability to make the necessary preparations for a no deal.
"And this could lead to a damaging and disorderly Brexit because without this bill passing we would not be able to retain the benefits of more than 40 existing trade arrangements; and neither will we have the means to protect consumers, industries and workers from being undercut by unfairly traded goods in a post-Brexit Britain."
Referencing her recent meeting with Donald Trump, Mrs May seized upon praise offered by the US president saying: "As president Trump has said, I'm a tough negotiator. And just as I made clear to him on Friday - I say to the British people today: I am not going to Brussels to compromise our national interest; I am going to fight for it. I am going to fight for our Brexit deal - because it is the right deal for Britain."
In his own newspaper article, for the Sunday Times, Mr Davis rejected suggestions the prime minister's proposals are the only viable Brexit path, as he voiced fears further concessions could be granted to Brussels.
He wrote: "This is an astonishingly dishonest claim. For the past seven or eight weeks my erstwhile department had been working on a white paper based on the prime minister's speeches.
"The individual chapters of the paper were being painstakingly agreed with individual departments of state before the whole paper was to be put to the cabinet - which, of course, it never was."
Former minister Steve Baker joined Mr Davis in quitting the Department for Exiting the EU in protest at Mrs May's plan.
He told the Sunday Telegraph the government is now in a "pathetic" position of "supplication" to the EU.
On Mrs May's presentation of her proposals at Chequers, Mr Baker said: "It does appear to me that there has been a year's worth of cloak and dagger to land us into the Chequers position.
"An establishment elite who never accepted the fundamental right of the public to choose democratically their institutions are working towards overturning them."
Mr Rees-Mogg, who leads the European Research Group of Tory eurosceptics, made his first direct attack on the prime minister.
Writing in the Sunday Express, he accused Mrs May of being so "oddly secretive" in her "headlong retreat that even key secretaries of state didn't know".
He added: "She always wanted a soft Brexit."
As Tory infighting over Brexit continues, the party has slumped six points in an Opinium poll.
According to the survey, Labour has opened up its biggest poll lead over the Conservatives since last year's snap general election.
Source: Sky News
