In a keynote address to the Lib Dem spring conference in York, Mr Farron accused the Prime Minister of pursuing the same "aggressive nationalistic" agenda as Donald Trump, Vladimir Putin and the French National Front leader Marine Le Pen.
He set Lib Dems the aim of supplanting Labour as the main party of opposition, and he warned Tories in seats where there was strong support for Remain they would be targeted in the same way as Zac Goldsmith in the Richmond Park by-election unless they defected.
Mr Farron said Mrs May was part of an "emerging consensus" on the political right characterised by nationalism, authoritarianism and protectionism, committed to reversing human rights and indifferent to or in denial of climate change.
"The politics of Trump. Of Putin. Of Le Pen. And now the politics of Her Majesty's Government. Welcome to the new world order. This is the new normal, the new status quo," he said.
"Aggressive. Nationalistic. Anti-Nato. Anti-EU. It is the post-war internationalist consensus unravelling in real time. Winston Churchill's vision for a world that achieves peace through trade, common values and shared endeavour evaporating before our eyes."
While he acknowledged voters had backed Leave in last year's EU referendum, he said it was Mrs May's choice, urged on by hardline Brexiteers, to take the UK out of the single market, with damaging consequences for British business.
"The Conservative Party has been taken over by its own version of Momentum. May's Momentum," he said.
"The hard Brexiteers. The anti-free trade protectionists. The shrink-the-state extremists. The anti-immigrant, anti-refugee, anti-international aid zealots. It's their party now, and it's hard to be sure whether Theresa May is their leader or their captive."
With the present Labour leadership "indifferent" towards the EU, Mr Farron said the past four prime ministers - David Cameron, Gordon Brown, Tony Blair and Sir John Major - all now had more in common with the Lib Dems than their own parties.
And in a direct appeal to Conservative MPs, he urged them to stop supporting policies in Parliament which were the opposite of what they signed up for.
"You are now the supporters of a Government that is as anti-business as Jeremy Corbyn. You are now the cheerleaders of a Government that is as anti-refugees as Nigel Farage," he said.
"You know it's wrong, so for pity's sake, have some self-respect. Defect or resign. If you don't, then when the next election comes we will do to you what we did to Zac Goldsmith."
He said that business leaders too should drop their support for a party which had abandoned its free market, internationalist, pro-business outlook and was engaged in "economic vandalism".
"Theresa May has put at risk the very people who have bankrolled her party's success for years. And she didn't have to. So business should drop the Conservative Party like a hot brick," he said.
With Labour incapable of taking seats from the Conservatives, he said that only the Liberal Democrats could deny them another majority at the next general election.
"We can gain the seats to rob the Tories of their power to wreck Britain. And by doing so we can change the course of our country," he said.