"We cannot and must not pretend things can continue as they are," she said.
The terrorists are not connected in their networks but they were "bound together by the single ideology of Islamist extremism which preaches hatred, sows division and promotes sectarianism", she said.
She said defeating this "perversion of Islam" was one of the "great challenges of our time". But it could not be defeated through military intervention alone.
"It will only be defeated whe we turn people's minds away from this violence", convincing them that "pluralistic British values" were superior.
In addition, Islamist-inspired extremism must be deprived of "safe spaces" - both online and physical - that it needed to flourish, she said. International agreements to regulate cyberspace, as well as work within the UK, was necessary.
Military action in Iraq and Syria was helping to destroy ISIS but she said there is "far too much tolerance" within the UK, which needs to become "far more robust in identifying and stamping out" extremism.
"That will require difficult and often embarrassing conversations," she said. She called for the country to stop living in "segregated communities" but to band together to stop the threat.
May said the current British counterterrorism strategy was robust, and had disrupted five "credible plots" since the March attack at Westminster Bridge.
But in the face of the changing threat the strategy would be reviewed.
"If we need to increase custodial sentences...even for less serious crimes, that is what we will do," she said.
"It is time to say enough is enough."
May added that while Labour and the Conservatives had suspended their election campaigns for the day, terrorists "can never be allowed to disrupt" the democratic process and campaigning would resume in full on Monday, with the general election to go ahead as planned.
