'Hasn't sunk in'
Later she attended joined a vigil outside Finsbury Park Mosque, held close to the scene of the attack.
Chairman of the mosque, Mohammed Kozbar, addressed the large crowd, saying the attack was "on our families, on our freedom, on our dignity".
He said the man who died was a father of six children.
Image copyright PA It is the fourth terror attack in the UK in three months, after incidents in Westminster, Manchester and on London Bridge.
Prime Minister Theresa May said the attack is "every bit as sickening" as the others.
"It was an attack that once again targeted the ordinary and the innocent going about their daily lives - this time British Muslims as they left a mosque having broken their fast and prayed together at this sacred time of year," she said.
After speaking outside Downing Street, the prime minister visited Finsbury Park Mosque, which is also close to the scene of the incident, where she held talks with faith leaders.
Labour leader and Islington North MP Jeremy Corbyn also visited the area, telling the BBC that "an attack on a mosque, an attack on a synagogue, an attack on a church is actually an attack on all of us".
At the sceneBy Cherry Wilson, BBC News
Locals say this is a proudly multicultural area, where the biggest rivalry is whether you support Arsenal or their north London rivals, Tottenham.
Now the mood here is one of shock, as residents stand by the police cordon seeing the aftermath of yet another attack in London.
Mother-of-four Nicola Senior, 43, is walking back from taking her children to school when she stops to take in the scene.
She said: "I'm frightened. Is there going to be retaliation?
"I am fearful for my kids. Can we go to the park? Can we go to the church? It feels like this is happening all the time."
The driver of the van was detained by bystanders before police arrived.
People at the scene said he had told them he wanted to kill Muslims.
The imam of Muslim Welfare House said a passing police van was flagged down.
Mohammed Mahmoud told reporters: "We told them the situation - there's a man, he's restrained, he mowed down a group of people with his van and there is a mob attempting to hurt him and if you don't take him then, God forbid, he might be seriously hurt.
"We pushed people away from him until he was safely taken by police."
Toufik Kacimi, chief executive of Muslim Welfare House, said the suspect had told those holding him "you deserve it" and was also saying "I did my bit".
A dangerous juncture in the battle against extremismBy BBC security correspondent Frank Gardner
This incident risks playing right into the hands of those planning further attacks on vulnerable citizens in the UK.
Online followers of the so-called Islamic State have been quick to seize on the Finsbury Park attack as proof of what they see as widespread hostility towards Muslims who live in the West. Inevitably, it will be used by recruiters and propagandists to incite further attacks - extremism breeds extremism.
The one thing that far right anti-Muslim extremists and violent jihadists have in common is the belief that peaceful coexistence between Muslim and non-Muslim is impossible.
The unified prayers and solidarity across communities that followed recent terror attacks are anathema to them. Extremists of both types want instead to divide society and will keep trying to bring this about by criminal acts of provocation such as this.