Officers said they were called to the house in Edmonton following reports of a man armed with a knife, and found the woman's body in the garden. She was named as 82-year-old Palmira Silva, who detectives believe is of Italian descent.
"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," said Detective Chief Inspector John Sandlin, who is leading the investigation.
He declined to confirm reports that the woman had been beheaded, or say what weapon was used in the attack.
Police said a man, 25, had been arrested on suspicion of murder by armed officers at the scene after they used a stun gun. One officer suffered a suspected broken wrist during the arrest.
Earlier, there was an attempt to attack two other people at a house on the same street but they escaped unharmed.
The reported nature of the killing had prompted speculation that the murder might be a terrorism incident after last year's gruesome murder of a British soldier in London, and the recent release of videos by Islamic State jihadists showing two US journalists being beheaded apparently by a British national.
"This is was a highly visible attack in broad daylight on a residential street," said Sandlin in a statement. "I can understand why this may cause people concern, however we are confident that we are not looking for anyone else at this stage."
