Palmira Silva, 82, who is believed to be of Italian descent, was found dead outside a house in Edmonton, north London.
Tributes were paid to Ms Silva, who is thought to have worked in a nearby cafe, as a 25-year-old man held in connection with the killing remained under police guard in hospital.
The man was Tasered and arrested on suspicion of murder at the scene in Nightingale Road by armed officers, some of whom were injured in a struggle.
Witnesses described seeing a man dressed in black, waving a machete-like weapon as he wandered screaming and shouting through private gardens.
A neighbour who knew Ms Silva said the widow was "such a sweet lady" who had lived in the house for more than 25 years and still went to work every day.
The neighbour, who did not want to be named, said she was "devastated" by what had happened.
She said: "I was speaking to her yesterday. She was weeding in the front garden, she loved her gardening.
"She was sitting having a rest.
"I said 'You've been doing such hard work, your flowers are beautiful'. She said 'I know'.
"I think maybe today she was in the back garden.
"She was such a sweet lady. She was slow getting around but she still went to work. I think really after her husband died that's what kept her going."
The house in the busy street where Ms Silva's body was found was the scene of a major police operation that continued into the night.
Scotland Yard revealed that its officers distracted the man after he was seen going through back gardens in Nightingale Road to prevent him attacking anyone else while they evacuated people from nearby homes.
Officers from the Met's homicide and major crime command are also investigating an attempted attack on two people at another house in the road before Ms Silva was killed.
A spokesman said: "At this stage we believe they were both able to get out of the house without injury."
Neighbours described the terrifying scene as events unfolded in the north London suburb shortly after 1pm yesterday.
Restaurant worker Freda Odame, 30, said she was about to go to sleep after working a night shift when she heard a commotion.
She said: "I heard shouting and banging and I opened my curtains and saw a guy holding a knife in a back garden a few doors along.
"He was screaming, I couldn't make out the words. I could see he seemed aggressive. He looked a bit frantic."
She said the man was waving a weapon around towards the floor.
"It was like he was looking for something on the floor," she said.
"I was shaking and I just shut the curtains. I was worried he might see me.
"Then the police knocked on the door and said 'You've got to get out, you've got to get out'."
Ahmed Yusuf, 19, said: "At first there were two police cars, then all of a sudden there were 20.
"The police said to drop everything. I said 'What's going on?' and they said there's a guy jumping over gardens."
Another local resident described seeing a man brandishing a machete and shouting about cats.
The witness, who did not want to be named, said he also saw a headless cat as he watched the drama from his window.
The man said: "There was a scream so I went to the windows and saw a guy with a machete with blood dripping from it.
"We saw a cat on the floor without a head.
"He was standing in the garden and walking up and down shouting about cats. I don't know why he was looking for a cat."
The knifeman then appeared in the witness's garden and began swiping at plants, he said.
He went on: "He started cutting roses. We were just trying to call the police. You can't think anything in that situation.
"He asked our neighbour if he had seen a cat and the neighbour was afraid and walked inside."
At one point the man climbed on top of a garage, he said.
"He appeared in the alleyway and I saw him raising the machete," the man said.
"Then he came to a front door and nobody answered so he started to bash the windows."
Metropolitan Police commander Simon Letchford said police were trying to establish the attacker's motive, but there are no signs of a link to terrorism.
He said officers smashed house windows to get people out after the man had been "cornered" in a house.
He said: "They (the officers) did everything they could to evacuate people from those premises and clearly they were aware of what had happened and they put themselves in extreme danger to protect the public, to ensure that his behaviour was stopped as soon as it possibly could be."
He confirmed that police were called to the scene by initial reports of a man attacking an animal, a cat or a dog, at 1.07pm.
A weapon was recovered at the scene but he did not reveal what it was, or the nature of Ms Silva's injuries.
Staff in shops around the cafe Ms Silva ran were stunned by the news of the killing.
Silva's Cafe in Church Street, near Edmonton Green station, was shuttered up as local people tried to come to terms with the tragedy.
Dilek Solma, 19, working behind the counter in a fruit and vegetable shop next door, said: "I'm so upset. She was a very smiley lady, always had a smile on her face, and loved the community. If somebody dropped something in here, she would help pick it up. Although she was 82, she was younger than me, and I'm 19."
She had known Ms Silva for three years, since she started working in the fruit and vegetable store. "She would come in to buy mushrooms and things like that, say 'the weather's nice', those sort of conversations.
"I don't know what the world's coming to. Whoever did it must be mentally ill, you can't do that sort of thing on purpose."
Sales assistant Raj Thangavelselvaraj, 50, who works in a newsagent next to the cafe, said: "She would come in to buy greetings cards for her grandchildren. She was a nice lady, she was a good lady to everyone. It's very sad."
One of his customers, John Harmer, 62, a retired clerical worker, said: "It's a very sad world. I didn't know her, but it's just unbelievable."