Police failures contributed to Dorothy "Cherry" Groce's death, whose shooting triggered the 1985 Brixton riots, a jury inquest has found.
Mrs Groce was shot by police looking for her son Michael and left paralysed from the waist down.
She died of kidney failure in 2011. Her son was never charged.
The Metropolitan Police Commissioner, Sir Bernard Hogan-Howe, apologised "unreservedly" for the shooting and the time it had taken to say sorry.
The jury at Southwark Coroner's Court found police failed to communicate properly and adequately check who was living at the property before the raid.
Following the inquest result, Sir Bernard apologised to her family for the years of suffering, saying the police operation had been inadequate and that the Met had failed to carry out its responsibilities properly.
Sir Bernard Hogan-Howe said it was "inexcusable" that it taken until now for the force to acknowledge.
The jury found there were eight failures made by police during the raid and her "subsequent death was contributed to by failures in the planning and implementation of the raid".
These included not properly briefing police officers that Mr Groce was no longer wanted by police, failing to adequately check who lived at the property or to carry out adequate observations on the house.
On the morning of the shooting, four children were present at the property.
The jury also concluded that officers should have called off the raid entirely during a police briefing but failed to do so.
However, they found there was no failure by police to call off the raid once it had begun.
The mother-of-eight died 26 years after the shooting in 2011, at the age of 63, from an illness which a pathologist directly linked to the gunshot injury.
Sir Bernard said, in a statement: "Sadly, this means that the person who most deserved to hear the apology, those words 'we are sorry', is no longer here.
"However, Cherry's children, her friends and others are here and they too deserve an apology. I am sorry for the years of suffering which our actions and omissions caused to your family."
Dr Robert Chapman said that during a post-mortem examination, he found small metal fragments from the bullet still lodged in the base of her spine.
Mrs Groce had also became more susceptible to a host of debilitating illnesses as a result of the injury, the court heard.
Her shooting by Metropolitan Police Inspector Douglas Lovelock sparked two days of unrest in Brixton during which shops were looted and petrol bombs thrown.
Mr Lovelock, who admitted being responsible for the wound, told the inquest he had apprehensions about going on the job and said he felt shocked when he mistakenly shot her.
He told the court that after shooting her he thought: "I hope to Christ it is shock and I have missed."
In a statement taken after the shooting and read to the jury, Mrs Groce said that as she lay bleeding, police continued to shout at her.
They asked her if she knew where Michael was, as they were searching for him in connection with an armed robbery.
Mr Lovelock stood trial in 1987 charged with inflicting unlawful and malicious grievous bodily harm and was acquitted.
After the hearing, Mrs Groce's son Lee Lawrence, who was 11 when he saw his mother shot, said:"I knew, she knew and we knew that what happened that day was wrong.
"After that shooting, my mum was left paralysed and we suffered in silence.
"The inquest has given us the only opportunity to get down to the truth about what really happened the day she was shot."