Palmira Silva was found dead in the garden behind a house in Edmonton in north London. The armed suspect ran through a number of back gardens in the street attacking a cat and a car.
The accused was later apprehended after a chase.
Scotland Yard officials helped save two young children by plucking them from inside their home as they chased the 25-year-old man, who was arrested with the help of a Taser gun and remains in hospital under police guard.
"This was a highly visible attack in broad daylight on a residential street. I can understand why this may cause people concern, however we are confident that we are not looking for anyone else at this stage," said John Sandlin, who is leading the investigation for the Metropolitan Police.
Ruling out any terrorism angle, Sandlin said: "Whilst it is too early to speculate on what the motive behind this attack was I am confident, based on the information currently available to me, that it is not terrorist related."
Specially trained family liaison officers will be deployed to support the family; we request that their privacy is respected at this very difficult time, he added.
While the police is yet to confirm the kind of weapon used in the attack, witnesses have reported seeing a man wielding a machete-like foot-long blade.
The Met is also investigating a linked attempted attack on two people in another address on the same road who managed to escaped unhurt from the house.
One line of inquiry for detectives is believed to be that the man was inspired by recent footage of terrorists beheading two American journalists in Syria.
A neighbour who knew the victim said the widow had lived in the house for more than 25 years.
"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," she told BBC.
Police officers had to distract the attacker to stop him from hurting anyone else while they evacuated families on the road.
They eventually cornered him inside one of the houses and one of the officers is believed to have broken his wrist during the scuffle.
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