Amber Rudd has quit Boris Johnson's Cabinet, with an outspoken attack on the way the government is managing the Brexit process.
The ex-work and pensions secretary said the government was having no "formal negotiations" with the EU about a new Brexit deal, only "conversations".
Instead, 80-90% of its time was spent preparing for an "inferior" no-deal option, she said.
Chancellor Sajid Javid said he was "saddened" by the resignation.
He told the BBC's Andrew Marr Show the government had been putting a "tremendous amount of effort" into getting a new deal with the EU.
He added that preparations for a no-deal scenario would "concentrate minds" in Europe regarding working towards a new agreement.
Downing Street has announced that Environment Minister Therese Coffey will replace Ms Rudd as work and pensions secretary.
Why did she leave?
In her resignation letter to PM Boris Johnson, Ms Rudd said: "I joined your cabinet in good faith: accepting that 'No Deal' had to be on the table, because it was the means by which we would have the best chance of achieving a new deal to leave on 31 October.
"However I no longer believe leaving with a deal is the government's main objective."
She also criticised the PM's decision to expel 21 MPs from the parliamentary Conservative party after they rebelled against him last week over a bill designed to avoid a no-deal Brexit, calling it an "act of political vandalism".
Having given up the Tory whip, the MP for Hastings and Rye, who supported Remain in the 2016 referendum, will remain an MP but will no longer sit as part of the Conservative party in Parliament.
"I will be considering my position - whether I will stand as an independent Conservative should there be an election coming up," she told the Sunday Times
What has the reaction been to her resignation?
Health Secretary Matt Hancock said the Conservative Party had "always been a broad church" and he was "gutted" to see Ms Rudd leave.
Former Foreign Secretary Jeremy Hunt said Ms Rudd's departure was "desperately sad news", describing her as "one of the most principled and capable ministers I've worked with".
Shadow Brexit secretary Sir Keir Starmer tweeted that her departure showed Mr Johnson's government was "falling apart".
Labour Party chair Ian Lavery said the resignation was a sign that "no one trusts" Mr Johnson. "The prime minister has run out of authority in record time and his Brexit plan has been exposed as a sham," he said.
SNP Westminster leader Ian Blackford called on the prime minister to resign, arguing he had "no support or credibility left".
"Boris Johnson's Tory government is on the verge of collapse - with no majority, no mandate and no right to pursue its reckless plans to impose an extreme Brexit," he said.