Darren Osborne, 48, received the life sentence for deliberately mowing down worshippers outside two mosques in north London "with a terrorist motive" shortly after 12.15am on June 19 past year.
The prosecution will ask the court to take account of the fact that this was a terrorist act when that sentence is decided.
Osborne hired the van in South Wales and drove it to London on Sunday 18 June planning to attack people attending the Al Quds Day march.
Osborne must serve a minimum of 43 years before being considered for parole.
"He was such a peaceful and simple man, he had no bad thoughts for anyone", she said.
He told his trial that he hoped to kill the leftist Labour opposition leader Jeremy Corbyn in the attack, as it would have been "one less terrorist off our streets", while killing Labour London Mayor Sadiq Khan as well "would have been like winning the lottery".
On June 19 previous year, Osborne drove his van intendedly into the worshippers leaving Finsbury Park Mosque after evening prayers in north London. "My heart was shattered when I saw my father lying in the morgue". The family's grieving process could not begin properly until the trial was concluded, she said.
The judge said Osborne, who lived in the Welsh capital city, Cardiff, had been rapidly radicalized over the internet by those determined to spread hatred of Muslims.
Mr Rees said it appeared to Ms Andrews that he was becoming brainwashed, and with the benefit of hindsight she described him a "ticking time-bomb".
"Before our father left the house that night he had spent the evening with his family, it was here where he felt most comfortable. He was very much a family man. this is how he will be remembered".
Sharif Xamza, who was struck from behind as he was kneeling next to Mr Ali giving him first aid, said "it was human to try to help another human - and then you too become a victim of attack". "My father will never be forgotten. His laughter will echo the walls of our home and his smile will be reflected in our eyes". He is also reported to have said "God bless you, thank you", as he was taken away.