She was speaking after chairing a meeting of the government's emergency Cobra committee in the aftermath of a terror attack in which a man died and 10 others were injured when a man drove a van into worshippers outside the Muslim Welfare House in north London.
Eight people were taken to hospital after the attack outside the mosque, which is also a community centre.
A 48-year-old man has been arrested on suspicion of attempted murder.
Prime Minister May said the driver of the van acted alone, adding: "Hatred and evil of this kind will never succeed."
She also said that police declared it a terrorist incident within eight minutes, and that it was "an attack on Muslims near their place of worship".
May added that "there has been far too much tolerance of extremism over many years".
"It is a reminder that terrorism, extremism and hatred take many forms; and our determination to tackle them must be the same whoever is responsible."
Today's attack his is the fourth terror attack in the UK in four months, after incidents in Westminster, Manchester and on London Bridge.
Police said all the victims of the attack, which was in the area of Finsbury Park Mosque, were Muslim.
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