Family of a mother and son who were shot through their front door by the Plymouth attacker have voiced anger at police for reinstating his gun licence weeks before the mass shooting.

Jake Davison, 22, shot dead five people including his mother on Thursday before turning the gun on himself. He also shot and wounded a 55-year-old woman and her son, 33, who lived near the house Davison shared with his mother in the suburb of Keyham.

The son had briefly opened his front door after hearing shots outside but closed it again when Davison took aim and fired. The son suffered stomach wounds and his mother was injured in the hand. “If he [the son] hadn’t slammed the door, he’d be gone,” a relative told the Guardian. The door has since been boarded up.

The relative, who asked not to be named, spoke of the family’s fury at Devon and Cornwall police for returning a gun licence to Davison last month after revoking it in December after he got into a fight.

“That should never have happened,” the relative said. “The family are angry about it but they don’t want to talk to the media. He [Davison] was known to the police and they gave a gun licence back to him, that’s fucking ridiculous.”

He said his family members were recovering from their injuries. “They’re angry but they are also thinking they are so lucky because they’re the survivors,” he said.

Ken Slate, 56, a friend of the injured mother, said he briefly spoke to her on Sunday. “She said she was not very well, she was shot in the hand and her son was shot in the side,” he said. “I think they are both trying to blank it out.”

Slate also knew Davison’s mother, Maxine, and confirmed she had tried to get mental health help for her son. He said: “I’m furious for Maxine, because she was let down by the adult social care [services]. She’d been trying for years to get some psychological help for her son – he had psychological problems since he was at school. He was a loner, he had autism. I never thought he’d do this, but something made him flip.”

Slate also questioned why the police returned a gun licence to Davison. “The police are supposed to do checks. If they’d checked with his GP they would have known that he [Davison] had psychological problems. So why give someone like that a gun?” Police and Plymouth council have been approached to comment.

A spokesperson for Livewell Southwest, an organisation that manages mental health services in the area, said: “We’re not aware of any of our mental health services receiving any contact from Jake or any members of his family in the days prior to the incident.

Davison, who held a gun licence for at least three years for sports use, frequently aired misogynist views and hatred for his mother on subreddit forums used by so-called incels – men who express hostility to those who are sexually active, especially women. The incel online subculture has been linked to a series of mass killings across the world.

On Friday the Independent Office of Police Conduct began an investigation into the decision by Devon and Cornwall police to reinstate the gun licence. At the weekend the government announced that all applicants for permission to own a firearm would be subject to social media checks.

Tracey Clarke, 45, a sheltered housing carer who described Maxine Davison as her best friend, said: “She always said Jake had mental health issues. She did say to me that lockdown affected him really badly, he’d delve into stuff to do with the virus.”

She said Davison had rowed with his mother after turning the front room of the house they shared together into a weight-lifting room, from where Davison posted videos to his YouTube channel.

She said: “He’d taken over her front room as a gym. She wanted to use it to watch telly and chill out and relax in. He said: ‘I’ve got to have it because gyms are closed.’ She wanted him to put it in the bedroom but he said it wasn’t going to fit. She’d do everything for him, he was bit demanding or coercive.”

Clarke added: “Giving back a gun to someone with mental health problems was stupid. It’s just asking for trouble.”