The chief constable of the Devon and Cornwall force, Shaun Sawyer, said Jake Davison, 22, had a firearms licence in 2020 but it was not clear whether it related to the weapon he used in his attack.
Officers have been told the weapon was a “pump-action shotgun” and although a weapon has been retrieved they are yet to confirm if that was the case, Sawyer said.
At a press conference in Plymouth, Sawyer said Davison murdered a 51-year-old woman known to him at an unidentified address in Biddick Drive on Thursday night before leaving the property and shooting dead the three-year-old girl and a 43-year-old male relative of the girl.
Davison then shot two other people, a man and woman aged 33 and 53 respectively, in Biddick Drive. They are in hospital with significant but not life-threatening injuries.
He then entered adjacent parkland where he shot a 59-year-old man, who died at the scene, Sawyer said. Then, in Henderson Place, Davison shot a 66-year-old woman who later died at Derriford hospital in Plymouth.
It took six minutes for the police to arrive on the scene, Sawyer said. He said terrorism was not the focus, but officers still had an “open mind”.
In videos posted to social media, Davison discussed being “beaten down” and “defeated by life”. Under the name Professor Waffle, he said he did not have “any willpower to do anything any more”, in a recording dated 28 July, and discussed the misogynistic “incel” movement.
Although Davison said he did not “clarify” himself as an “incel” – the abbreviation used online for “involuntarily celibate”, for those unable to find a romantic or sexual partner despite desiring one – he spoke about “people similar to me have had nothing but themselves”.
His YouTube channel was subscribed to gun-related accounts and another named Incel TV. In another clip, he discusses missing out on a teenage romance and refers to “Chads”, an incel community term for good-looking men who attract women.
Sawyer said he could not say “at this time” whether Davison had mental health issues, but added: “This is an extraordinarily unusual response by a fellow human being.”
He said: “We are not considering terrorism or a relationship with any far-right group.”
A spokesperson for Babcock International, which has a significant presence near the city at the dockyards in Devonport, confirmed that Davison had worked for the company.
The firm’s CEO, David Lockwood, earlier said: “Our thoughts and condolences are with the friends and families of those involved in this tragedy. We stand with the city at this difficult time.”
Social media posts from about 2018 suggest Davison was a fan of Donald Trump and a supporter of the UK Libertarian party.
YouTube confirmed that an account belonging to Davison has been terminated for violating its offline behaviour policy.
Boris Johnson tweeted: “My thoughts are with the friends and family of those who lost their lives and with all those affected by the tragic incident in Plymouth last night. I thank the emergency services for their response.”
The Independent Office for Police Conduct (IOPC) said it had received a mandatory referral from Devon and Cornwall police relating to the incident.
David Ford, an IOPC regional director, said: “Our thoughts remain with all of the many people who will be severely affected. The referral relates to yesterday’s events as well as police contact with Jake Davison prior to the incident, including the force’s role and actions regarding firearms licensing. We are urgently assessing the matter to determine what further action may be required from us.”
The incident is the first mass shooting in Britain since June 2010, when Derrick Bird, a taxi driver, killed 12 people and injured 11 others in Cumbria.
• This article was amended on 13 August 2021 to clarify the Plymouth location of Babcock International.