The 40-year-old was found at an address in Globe Road, Bethnal Green, London, on Thursday afternoon.
Teachers raised the alarm when she did not collect her children from school, the Metropolitan Police said.
Residents said they were “shocked” by the death of the woman, who was “such a lovely person” and had lived in the area “a long time”.
Mohammad Shamin, 57, a local businessman, said: “She was always walking around with her boys, a good mother.
“And when they found her it was very sad.
“People here are shocked, such a lovely person.”
Another resident, who did not want to be named, said it was “chaotic” on Thursday.
“The police came and got in, they broke the door,” she said.
A couple, aged in their 30s, said: “We don’t know them that well because I suppose that’s how it is these days.
“But she seemed nice and the kind of person you would want as a neighbour, her kids were also very good.”
The woman, who was pronounced dead at the scene, has not yet been formally identified but her next of kin have been informed.
A post-mortem examination is due to take place.
Det Ch Insp Laurence Smith said: “A dedicated team of officers is working around the clock to trace the person responsible for this and my thoughts are with this woman’s family as they come to terms with their tragic loss.”
The force has appealed for anyone with information to contact officers on 101 or call Crimestoppers anonymously.