Deveca Rose had left her two sets of twins, aged three and four, in the locked terraced house when the blaze broke out on the evening of December 16, 2021.
The 30-year-old defendant, who had split up with her partner and suffered from mental health problems, was found guilty of four counts of manslaughter following an Old Bailey trial.
On Friday, Rose, who was on bail throughout her trial, sobbed with her head covered in the dock of Court One as she was sentenced by Judge Mark Lucraft KC.
In a televised hearing, the judge sentenced her to 10 years in prison.
Earlier, the boys’ father Dalton Hoath said losing his four sons – Leyton and Logan, aged three and four-year-olds Kyson and Bryson – was “the worst day of my life”.
In a statement read by a relative on his behalf, he said: “Their lives had just begun but were cut so short. It was every parent’s worst nightmare.
“I’m not a great talker but even if I was I could not put it in words. I simply want to join them.
“I will never recover from losing my funny, beautiful boys. I have to fight for all of us left behind and live with this massive pain in my heart before I meet them again.”
Great grandmother Sally Johnson wept in court and she told of the “horror” and “pain” of her loss.
She said: “The thought of them crying and screaming out will haunt me forever. My only comfort is they are now together forever and need never be alone again. I’m afraid I will never be able to forgive.”
Quoting her great grandsons’ favourite word, she said: “Why? Just why?”
Prosecutor Kate Lumsdon KC had told the court: “There was rubbish thickly spread throughout the house. The toilet and the bath were full of rubbish and could not be used. Buckets and pots were used as toilets instead.”
Rose had gone to the supermarket, leaving the boys at the rented home in Sutton, south-west London.
When a cigarette or tea light in the living room sparked a fire, the boys were trapped and ran upstairs calling for help.
A neighbour tried to break down the front door before firefighters in breathing apparatus went in and found the children’s bodies under beds.
They were rushed to two separate hospitals, but attempts to save them failed and they died from inhalation of fumes later that night.
Rose arrived home while firefighters were still tackling the blaze and she was taken in by a neighbour.
She had claimed she left the children with a friend called Jade, which prompted firefighters to go back into the house to search for her.
Police carried out extensive inquiries to find Jade and concluded she either did not exist or had not been at the house that day.
In police interviews, Rose admitted leaving the boys alone in the house on two earlier occasions.
Jurors were told that social worker Georgia Singh had raised concerns about the family, but the case was closed three months before the fire.
Previously, a health visitor had also expressed worries, but they were not followed up after she retired, jurors were told.
The children had not attended school for three weeks before their deaths.
Rose, of Wallington,, attended much of the trial by video-link from home on medical advice and declined to give evidence in her defence.
The court heard there was evidence suggesting she was probably depressed and may have suffered from a personality disorder, but the prosecution asserted that was not a defence.
In mitigation, her barrister Laurie-Anne Power KC highlighted that Rose had struggled with “complex psychiatric mental health needs”.
She told the court: “There is nothing I can say to mitigate the loss to the Hoath and Rose family.
“Even though she is criminally responsible for the deaths of those children, she has suffered the greatest loss of all.”
