British police named Osborne, a father of four living in the Welsh city of Cardiff, as the man who ploughed a van into pedestrians outside the Mosque on Seven Sisters Road in Finsbury Park, North London, yesterday.
He was detained by members of the public at the scene and then take to hospital and later arrestedon suspicion of the commission, preparation or instigation of terrorism including murder and attempted murder.
Nine others were taken to three London hospitals and two were treated for minor injuries at the scene, outside Muslim Welfare House, near Finsbury Park Mosque.
In a statement on behalf of the family, Osborne's 26- year-old nephew Ellis Osborne said, "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."
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Osborne's mother, 72-year-old Christine,said her son was "not a terrorist and had never shown any hatred towards Muslims".
"I'm at my wit's end. I saw him on TV and recognised him straight away. I just screamed. My son is no terrorist -- he's just a man with problems and I don't know how to cope with all this," she told The Sun.
Osborne's sister Nicola denied that her brother is political.
"He wouldn't even know who the Prime Minister is. I've never heard him say anything about Muslims or anything racist," she said.
He left Weston-Super-Mare several years ago and moved to a terraced house in Pentwyn, Cardiff, with his partner, children and two dogs.
The couple have four children, aged between 16 and five, and Osborne is described as a "family man".
Some neighbours believe he andhis partnerhad separated in recent months and that he was often seen shouting at her in the street.
Osborne, who was not known to the police or security services, is believed to have driven 15 miles from his home in Cardiff to Pontyclun Van Hire on Sunday, hiring an 80-pound- a-night van.
He allegedly hurled insults at his Asian neighbour's 12- year-old son and was allegedly thrown out of his local pub the night before the attack for "cursing Muslims".
Meanwhile, Scotland Yard chief Cressida Dick joined hundreds at a vigil outside Finsbury Park Mosque, where people from across the community had gathered in solidarity and to lay flowers.
The Finsbury Park attack is the fourth in the UK in four months, after incidents in Westminster, Manchester and on London Bridge.