The attack comes at a time of political turmoil in Britain, as May, weakened by the loss of her parliamentary majority in a June 8 election, plunges into divorce talks with the European Union.
She has faced heavy criticism for her response to a fire in a London tower block last Wednesday which killed at least 58 people, and for her record on security after a series of attacks blamed on Islamist militants in recent months.
"All my thoughts are with the victims, their families and the emergency services on the scene," May said, adding that she would chair an emergency response meeting later on Monday.
The mayor of London, Sadiq Khan, said extra police had been deployed to reassure communities, especially those observing Ramadan, describing the attack as "an assault on all our shared values of tolerance, freedom and respect".
The leader of the opposition Labour Party, Jeremy Corbyn, in whose constituency the attack took place, said he was "totally shocked".
The incident comes just over two weeks after three Islamist militants drove into pedestrians on London Bridge and stabbed people at nearby restaurants and bars, killing eight..
It 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.
Police had said hate crimes had risen after the London Bridge attack and they had stepped up their visible presence at places of worship.
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.
"It appears that a white man in a van intentionally ploughed into a group of worshippers who were already tending to someone who had been taken ill," the council said in a statement.
"HE TARGETED MUSLIMS"
Police said they were called just after 12:20 a.m. (2320 GMT Sunday) to reports of a collision on Seven Sisters Road, which runs through the Finsbury Park area of north London.
"From the window, I started hearing a lot of yelling and screeching, a lot of chaos outside ... Everybody was shouting: 'A van’s hit people, a van’s hit people'," one woman who lives opposite the scene told the BBC.
The Evening Standard newspaper said the van appeared to have been rented in Wales, although there was no immediate confirmation of this from the authorities.
Miqdaad Versi, assistant secretary general of the Muslim Council of Britain, said the van had deliberately swerved into a group of people who were helping a man who was ill and had fallen to the ground.
"Basically, a van swerved into them deliberately," Versi told Reuters, citing a witness.
He said the driver had run out of the van but a group of people caught him and held him until police arrived.
The Finsbury Park Mosque 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.
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.
Members of the congregation in the two mosques in the area are mainly from North and West Africa.
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