Announcing her decision to quit the government - on the eve of the European elections - the leader of the House of Commons said she no longer believed the Brexit deal will deliver a "truly sovereign United Kingdom".
It comes as pressure mounts on Ms May to resign as prime minister immediately, amid warnings her key Brexit legislation will be crushed once again when she brings it to the Commons in June for a fourth vote.
Ms Leadsom, who stood against Ms May during the 2016 Conservative leadership contest, posted her resignation letter on Wednesday evening, warning: "I no longer believe that our approach will deliver on the referendum result."
Just yesterday, the senior Brexiteer said she was "actively considering" and "preparing" a leadership bid for when the prime minister formally announces her resignation.
Explaining the timing of her decision to resign on the eve of polling day in the European elections, Mrs Leadsom said: "I considered carefully the timing of this decision, but I cannot fulfil my duty as Leader of the House tomorrow, to announce a Bill with new elements that I fundamentally oppose.
"I fully respect the integrity, resolution and determination that you have shown during your time as prime minister.
"No one has wanted you to succeed more than I have, but I do now urge you to make the right decisions in the interests of the country, this government and our party."
Ms Leadsom - a member of the so-called "Pizza Club" gatherings of Brexit-supporting ministers - also said there had been "such a breakdown of government processes that recent Brexit-related legislative proposals have not been properly scrutinised or approved by Cabinet members".
She added: "The tolerance to those in cabinet who have advocated policies contrary to the Government's position has led to a complete breakdown of collective responsibility."
In response to Ms Leadsom's decision to quit, a Downing Street spokesman said: "Andrea Leadsom has served with distinction and great ability as a member of the government, and the prime minister is grateful for all of her work.
"We are disappointed that she has chosen to resign, and the prime minister remains focused on delivering the Brexit people voted for."
Commenting on her resignation, Labour's chairman Ian Lavery added that Ms May's authority "is shot and her time is up".
"While the Tories are ripping themselves apart, our country is in crisis. The Government has made a catastrophic mess of the Brexit negotiations, our steel industry is under threat and universal credit is pushing people into poverty," he said.
"For the sake of the country, Theresa May needs to go, and we need an immediate general election."
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