The Home Secretary revealed the new "extremism disruption orders" would ban those who "spread hate but do not break existing laws" from the airwaves and make it easier to formally proscribe groups deemed to be linked to terrorism.
The orders will apply to those who “spread or incite hatred” of gender, race or religion as well as those who engage in “harmful activities” for the “purpose of overthrowing democracy”. That's prompted fears the laws could be used on non-violent political groups and the political enemies of those in power.
Critics said the powers were draconian and mocked the notion of banning those who are not proven to have broken the law, while human rights Liberty said the powers were "worthy of a caliphate".
The eurosceptic party that is jeopardising the Tories' chance of winning the next election - and to which two MPs and other prominent politicians have already defected - also suggested it could be banned with such an order.
Suzanne Evans, deputy chair of Ukip, told a fringe event at the Tory Party conference that the power could be used to close down her party, the BBC's Norman Smith reported.
Diane James, MEP and Ukip spokeswoman for home affairs, said: "May does not even specify who would be targeted and on what grounds, meaning anybody could be labelled as extremist. What we are left with could be abused to shut down free speech and discriminate against individuals and organisations disproportionately and without due cause."
Britain First, a far-right pseudo militia that invades mosques to protest against Islam, has also voiced disapproval.
"If this new law goes through, it will effectively mean the end of true democracy in this country," the group said in a typically breathless statement.
"The establishment is very cleverly using the threat of Islamic extremism to introduce laws that curtail the freedom of expression for everyone."
During May's speech, journalist and solicitor David Allen Green mockingly tweeted: "Theresa May likely to be outraged at this requirement of 'evidence' making it not possible to prosecute people for terrorism charges."
Theresa May likely to be outraged at this requirement of "evidence" making it not possible to prosecute people for terrorism charges.— Jack of Kent (@JackofKent) October 1, 2014
Two prominent Tories also criticised the powers within hours of the speech.
David Davis, the former shadow home secretary who once stood down to fight a by-election in protest at the erosion of civil liberties, said they were "incredible powers to limit democratic rights".
He told the BBC: "These are quite incredible powers to limit democratic rights, rights that people have had for 200 years in this country, and they are based on the Home Secretary having a reasonable belief - that's the test, not an evidential test, a reasonable belief - that an organisation will break certain criteria.
"And one of the criteria is a risk of harassment, alarm or distress. Well, one's tempted to say I do that to the Tory Party every day. This is really, really serious stuff.
"I think it will have real trouble both getting through the House of Commons and indeed real difficulty standing up in front of the court."
He added: "Deal with the violence, deal with the actions, deal with the measures. We didn't stop a whole load of people leaving here to go to Syria. Why didn't we do that? Those are the ways you deal with these things.
"We've got to be very careful that we don't end up like the people we're trying to defeat, forgetting what we're defending. We're defending a liberal democracy, one in which you can say all sorts of things."
Former attorney general Dominic Grieve QC, who lost his post in the July cabinet reshuffle, said the plans could be perceived as "draconian".
He told BBC Radio 4's World At One programme: "This can have the unintended consequence of not actually tackling correctly the problem which is arising, but simply fuel resentment and it's a very delicate balancing act between these two concepts that we have to pay attention to."
He added: "It's difficult to see how in practice some of these restrictions would operate without leading to the consequence that a person would end up being prosecuted for expressing a point of view which the Home Secretary has considered is extreme."
"I think any restriction on freedom of expression of individuals outside of the criminal law is something that has to be approached with very great caution."
Shami Chakrabarti, Director of Liberty, said: "She (May) gave a good sermon about human rights and the rule of law in the Middle East whilst mocking the Court of Human Rights and proposing to ban non-violent speech and organisations.
"How do you promote liberal democratic values by promising state powers worthy of a caliphate?"
David Cameron said the orders could involve a broadcasting ban similar to the one imposed on Sinn Fein during the 1980s - when the IRA-linked political party's spokespeople had lines read by actors if they quoted on the news.
He told Channel 4 News: "I don't want to name names but I think you've probably had on your programmes those people who perhaps go just one stop short of endorsing violence, but they are really inciting young British people into hatred that is leading to violence.
"We don't just say (Nazi extremist) Combat 18 is a bad thing, we think the National Front is a bad thing too, and we have to be as confrontational with this Islamist extremist terror."Suggest a correction