Jake Davison murdered his mother Maxine before shooting and killing four other people.
The mother of the Plymouth gunman, Maxine Davison, and three-year-old Sophie Martyn have been named among the five victims of his shooting spree.
Ms Davison, 51, was shot and killed by her 22-year-old son Jake Davison at her home on Biddick Drive, Plymouth, on Thursday evening.
Davison went on to kill three-year-old Sophie, her father Lee Martyn, 43, Stephen Washington and Kate Shepherd.
His attack lasted about six minutes before he turned the gun on himself.
In online videos Davison spoke of being “beaten down” and “defeated by life”.
All of those who died lived in the Keyham area of Plymouth, Devon and Cornwall Police said.
Officers are continuing to investigate 13 scenes within a cordon that is expected to remain in place throughout much of the weekend.
Having killed his mother, Davison left the property and immediately shot and killed Mr Martyn and his daughter on the street.
Stephen Washington, 59, was also killed, along with Kate Shepherd, 66, who was injured at the scene and died later at Derriford Hospital.
Prime Minister Boris Johnson said the issue of how Davison came to legally own a gun should be “properly investigated” as he described the shooting as an “absolutely appalling” incident.
Police said the incident, the worst mass shooting in Britain since 2010, was not terror-related. However, Davison made references to “incels” in some online social media videos.
Incels are members of misogynistic online groups of “involuntary celibate” men, who blame women for their sexual failings and who have been linked to a number of violent acts around the world.
Davison had posted hate-filled online rants about single mothers and about his own mother in particular, calling her “vile, dysfunctional and chaotic”.
Chief Constable of Devon and Cornwall Police, Shaun Sawyer, said Davison was a licensed firearms holder and witnesses described the weapon he used as a “pump action shotgun”.
The force has referred itself to the Independent Office for Police Conduct (IOPC) over the circumstances surrounding Davison’s firearms licence.
Local resident Bert Pinkerton told the BBC he walked past the gunman on the street.
“I looked down, walked around the corner, the bloke was walking towards me with a black rifle. I could smell the gunfire.”
He said Davison had a “vacant stare” and he felt lucky to be alive. “It could have been me,” he said.
Neighbour Paris and Billy told the BBC they were “heartbroken” to find out the youngest victim of the gunman was aged three.
Paris said: “I feel devastated for the family it makes everything worse being a child.
She added: “Nothing’s ever going to be the same especially when it’s over the road.”
Billy said: “Its going to be different here forever now I think.”
Flags in Plymouth are being flown at half-mast following the atrocity, while Smeaton’s Tower will be lit up as a mark of respect to the victims on Friday night.
There will be a candlelit vigil at 9pm on Friday in North Down Crescent Park to pay tribute to those who were killed.
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