Shortly after midnight, the vehicle swerved into a group of people leaving prayers at the Muslim Welfare House and the nearby Finsbury Park Mosque in north London, one of the biggest in the country.
The driver, a 48-year-old white man, was grabbed at the scene by locals and pinned down until police arrived.
"This morning, our country woke to news of another terrorist attack on the streets of our capital city: the second this month and every bit as sickening as those which have come before," May told reporters outside her Downing Street office.
"This was an attack on Muslims near their place of worship," said May who later visited the mosque.
The attack is the fourth since March in Britain and the third to involve a vehicle deliberately driven at pedestrians.
It also comes at a tumultuous time for the government with Britain starting complex divorce talks with the European Union and May negotiating with a small Northern Irish party to stay in power after losing her parliamentary majority following a snap election.
The mosques' worshippers, who come mainly from North and West Africa, had just left special prayers during the Muslim holy month of Ramadan. Abdulrahman Aidroos said he and his friends had been tending an old man who had suffered a heart attack when the van was driven at them.
"He was saying 'I wanna kill more people, I wanna kill more Muslims'," Aidroos told BBC TV. He said he had helped tackle and detain the driver while other witnesses said the imam had stepped in to ensure the man was not harmed.
"Their restraint in the circumstances was commendable," said Neil Basu, senior national co-ordinator for counter-terrorism policing. The man was arrested on suspicion of attempted murder and police said they believed he had acted alone.
"I would like to ... thank our imam, Mohammed Mahmoud, whose bravery and courage helped calm the immediate situation after the incident and prevented further injuries and potential loss of life," said Toufik Kacimi, the chief executive of the Muslim Welfare House.
Police said 10 people were injured, with eight taken to hospital, two in a very serious condition.
The man who was being given first aid at the scene before the attack had died but it was not clear whether his death was directly linked.
Usain Ali, 28, said he heard a bang and ran for his life.
"When I looked back, I thought it was a car accident, but people were shouting, screaming and I realized this was a man choosing to terrorize people who are praying," he told Reuters. "He chose exactly the time that people pray, and the mosque is too small and full, so some pray outside."
Just over two weeks ago three Islamist militants drove into pedestrians on London Bridge and stabbed people at nearby restaurants and bars, killing eight..
The latest incident also follows a suicide bombing at a pop concert in Manchester, northern England, in May which killed 22, while in March, a man drove a rented car into pedestrians on Westminster Bridge in London and stabbed a policeman to death before being shot dead. His attack killed five people.
May, weakened after losing her parliamentary majority in a June 8 election she had called to strengthen her hand in Brexit talks, has faced criticism for her record on security after the previous series of attacks blamed on Islamist militants.
She has also been criticized for her response to a fire in a London tower block last Wednesday which killed at least 79 people.
"Today’s attack falls at a difficult time in the life of this city, following on from the attack on London Bridge two weeks ago – and of course the unimaginable tragedy of Grenfell Tower last week," May said.
She promised action to stamp out all forms of hatred, saying there had been far too much tolerance of extremism in Britain over many years.
Police had said hate crimes rose after the London Bridge attack and more officers would be deployed to provide reassurance to mosques.
The Muslim Council of Britain said Monday's attack was the most violent manifestation of Islamophobia in Britain in recent months and called for extra security at places of worship.
Finsbury Park Mosque said it was a "callous terrorist attack" and noted it had occurred almost exactly a year after a man obsessed with Nazis and extreme right-wing ideology murdered lawmaker Jo Cox, a former humanitarian aid worker.
The mosque itself gained notoriety more than a decade ago for sermons by radical cleric Abu Hamza al-Masri, who was sentenced to life in a U.S. prison in January 2015 after being convicted of terrorism-related charges.
However, a new board of trustees and management took over in February 2005, a year after Abu Hamza was arrested by British police, since when attendance has greatly increased among worshippers from various communities, according to the mosque's website.