The Prime Minister said there had been “far too much tolerance of extremism” in recent years, including anti-Muslim hatred.
Mrs May said: “Terrorism, extremism and hatred take many forms, and our determination to tackle them must be the same, whoever is responsible.
“This Government will act to stamp out extremist and hateful ideology, both across society and on the internet.
“We will be reviewing our counter-terrorism strategy and ensuring that police and security services have the powers they need.
“And we will establish a new commission for countering extremism in the same way that we have fought racism.”
The PM made the comments outside Downing Street after chairing a meeting of the Government’s emergency Cobra committee.
Meanwhile, Labour Party leader Mr Corbyn arrived at the scene in Finsbury Park which sits inside his north London constituency.
He was said to be “overcome” with emotion and “distraught” as he spoke to religious leaders in the area.
Mr Corbyn said: “Together, our community will get through this tragedy.”
Mrs May added: “This was an attack on Muslims near their place of worship.
“And like all terrorism in whatever form, it shares the same fundamental goal.
“It seeks to drive us apart and to break the precious bonds of solidarity and citizenship which we share in this country. We will not let this happen.”
Cabinet minister Sajid Javid, who is Muslim, spoke briefly to concerned residents as he visited the scene of the attack this morning.
He said: “The perpetrator of this attack, and those terrible attacks that we saw recently in Manchester and London, their intention is to seek to divide society.
“My message to them is that they will always, always fail.
“This Government will always take a zero-tolerance approach to hate crime, including anti-Muslim hate crime, wherever we find it.”