Mrs May said that the attack on Muslims was "every bit as insidious and destructive to our values and our way of life" as the recent string of terror attacks apparently motivated by Islamist extremism, adding: "We will stop at nothing to defeat it".
"Today we come together, as we have done before, to condemn this act and to state once again that hatred and evil of this kind will never succeed".
"He has further been arrested for the commission, preparation or instigation of terrorism, including murder and attempted murder", Scotland Yard police headquarters said in a statement.
Police said a suspect was arrested immediately after the attack, which is being treated as a terrorist incident.
The white van ploughed into pedestrians as the area was busy with worshippers attending Ramadan night prayers in Seven Sisters Road.
Eight injured people were treated in hospital, and two others were treated at the scene, he said.
Nine other people were injured, while the attacker has been taken into police custody.
"Everyone was shouting "a van's hit people", she said.
The site of the incident is close to another mosque near the Finsbury Park on the same road.
Several bunches of flowers had been deposited outside the mosque as commuters went to work on Monday morning.
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The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire. She told BBC One's Sunday Politics: "We are still hearing stories of people not being allocated properly".
"The van literally turned left with no indication, with no even, like suddenly, deliberately left, and then just hit the people", said one eyewitness.
London's Muslim mayor, Sadiq Khan, condemned the incident as a "horrific terrorist attack on innocent people".
London Ambulance Service deputy director of operations Kevin Bate said: "We have sent a number of ambulance crews, advance paramedics and specialist responses teams to the scene". Police said a man who was driving the vehicle has been arrested and taken to a hospital as a precaution.
The incident occurred in North London outside of the Muslim Welfare House, which is located near the Finsbury Park Mosque.
He has been taken to hospital as a precaution and is due to receive a mental health assessment.
The police investigation into the incident is being carried out by the Met's Counter Terrorism Command.
He added: "There were at least 300 people in the mosque praying, and everyone was panicking, everyone was screaming".
The Metropolitan's Commissioner, Cressida Dick, said, "London has woken up to the news of another appalling attack on our city".
Britain's terrorist alert level is now at "severe", the second-highest level, meaning an attack is highly likely.
And in March, a driver plowed into pedestrians on Westminster Bridge, causing four deaths, then exited the vehicle and stabbed a police officer to death. In May, the city of Manchester was targeted with a suicide bombing at a pop concert that killed 22 people.
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