Speaking on radio station LBC, Ms Miller asked how Britons could have “any confidence” in Mrs May when she would not even debate with other party leaders.
She added the prime minister had offered “no detail or debate” about how the country will move forward during and after Brexit.
“This whole idea of the will of the people… people want debate,” she said.
“How can we have any confidence in Mrs May to negotiate, and not just with our EU exit and new relationship, but on the wider world stage and new trade deals when she won’t even debate with leaderships of our own national parties.
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Gina Miller said Theresa May needed to defend why she called the General Election
How can we have any confidence in Mrs May to negotiate
“Actions are speaking louder than words and I think we should all be really alarmed by this.
"It’s Mrs May who called this election… and she should be able to defend why she did it.
"She should be able to clearly say to the British public, ‘this is what I stand for, this is what this election is about and this is my plan going forward.'
"When it comes to answering questions about the plan as we go forward, there has been no detail or debate about that.
Ms Miller added the public was crying out for more detail, which had not been offered by the prime minister.
"There has been empty promises but no backing up on the plans of how we actually get to the strong and stable economy and strong and stable leadership," she said.
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May meets Juncker and Barnier at Number 10 Wed, April 26, 2017
Theresa May hosted European Commission President Jean-Claude Juncker and chief negotiator Michel Barnier at Downing Street for the first face-to-face talks since she triggered the two-year process of withdrawing from the EU
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Prime Minister Theresa May greets European Commission President Jean-Claude Juncker ahead of a working dinner at 10 Downing Street, London
"I can't see any details and that's what the public is asking for."
Meanwhile, a europhile has donated thousands of pounds to Gina Miller’s anti-hard Brexit campaign group, Best for Britain.
Figures released by the Electoral Commission earlier this month revealed that Anatole Kaletsky donated £20,000 to Best for Britain in the second week of campaigning.
The donation came after the economist urged the European Union to “persuade Britain to change its mind about Europe” as he claimed those who had voted for Brexit in the referendum were “divided in their aims”.
The Best for Britain campaign was launched by Mrs Miller in April in a bid to help General Election candidates who are prepared to help block Brexit depending on the deal agreed with Brussels.