The family of the man being held after the Finsbury Park attack have said he had been "troubled for a long time".
Darren Osborne was arrested after worshippers were targeted by a man driving a van near Finsbury Park Mosque in north London early on Monday.
Neighbours of the father-of-four from Cardiff said they were "shocked" when they saw pictures of him being arrested but one revealed he had called her Muslim children "inbred" and another said he rang the police after spotting a man he believes was Osborne sleeping in a van on Saturday night.
In a statement, Osborne's family said he had been "troubled for a long time".
"We are massively shocked. It's unbelievable. It still hasn't really sunk in.
"We are devastated for the families. Our hearts go out to the people who have been injured."
They said the 47-year-old was "not a racist" and had never expressed racist views, adding: "It's madness. It is obviously sheer madness."
The attack unfolded as a man who had been taken ill was receiving first aid from the public near the mosque, where people had been saying Ramadan night prayers. The van was driven at people who were helping him.
The man was pronounced dead at the scene and paramedics took nine people to three London hospitals while two others were treated for minor injuries.
Witnesses described hearing the driver, who was detained by members of the public before police arrived, shout: "I am going to kill Muslims."
Osborne was arrested on suspicion of attempted murder but Scotland Yard said he was later arrested for the commission, preparation or instigation of terrorism, including murder and attempted murder.
Images of the van showed it was rented from Pontyclun Van Hire, near Cardiff.
One of Osborne's neighbours, Edward Gardiner, 28, a self-employed builder and plumber, called police at 12.27am on Sunday morning to report concerns for the welfare of a man sitting in a Pontyclun Van Hire vehicle.
The man, who smelt of drink, was sleeping across the front three seats of the van with the door open, close to Osborne's home.
"I called police because I saw a random van in my cul-de-sac with someone drunk in it and the door open," Mr Gardiner, who lives in a nearby property, said.
"I could smell alcohol on him and he was grunting and groaning. I poked him but he didn't respond so I called 101. I gave them the reg, it was a 64 reg.
"It was a Pontyclun Van Hire van. They said they would sort it out. They didn't give me a crime reference number, I don't know if they came out.
"I thought it was some random drunk guy who wanted to pull over to have a kip. I thought someone should go and check on him.
"I didn't think anything about it but then I saw the news reports and it was the same guy, the same van."
It also emerged that Osborne had been asked to leave the nearby Hollybush pub on Saturday night after arguing about immigration.
Pub regular Phil Henry said: "He was kicked out of here, the landlord said, for shouting about Islam. He was asked to leave quietly and he went.
"He came in here and he was just staring before he started shouting.
"When he came in the landlord said he was on his own and started shouting 'I'll kill every f****** Muslim'.
"They said 'We don't want to hear that' and he just left of his own accord."
Mr Henry said the community was "absolutely shocked" and that it was a mixed community where he had never seen any trouble.
"It is a cosmopolitan city and always has been," he said.
"It hasn't happened on our own doorstep but it has because the guy comes from here. We don't want to be linked to it."
Neighbours said Osborne had been living in a tent in woodland after being kicked out of the family home.
Khadijeh Sherizi, who converted to Islam in 2003, said Osborne was polite and her children, who are Muslim, would play with his children most days.
But on Saturday, Osborne approached Mrs Sherizi's eldest son, 12, and called him "inbred". The following day, Osborne repeated the insult to Mrs Sherizi's 10-year-old daughter.
"We are Muslim but I am white," Mrs Sherizi said.
"It is shocking what he has done, for him to drive down Muslims. He was just so normal. We never had a problem with him, nothing.
"In Cardiff, it can be quite racist. Sometimes I feel threatened with my veil on. I know exactly what people are thinking by their looks.
"But there has been nothing from him (Osborne), no threats, no animosity at all."
Asked about Mr Gardiner's claims, South Wales Police confirmed they were called to a report of an insecure van parked on a street in the Llanedeyrn area of Cardiff, 24 hours before the attack in London.
In a statement released on Tuesday afternoon, the force said officers responded to a call at 12.27am on Sunday, June 18.
They said: "Officers attended, a male was asleep inside the vehicle, which showed no signs of having been driven recently.
"The officers' assessment was that no offences were disclosed.
"This is a significant investigation and anyone with any information is asked to call the police confidentially on 0800 789 321."