Brunt asked Leyland why she was using her Twitter account to attack the McCanns, who live in Rothley, Leicestershire. "I'm entitled to do that," Leyland replied.
When Brunt told her that she had been reported to police, she replied: "That's fair enough."
Footage of the encounter aired on Friday and the next day it was reported that Leyland had left the village.
A neighbour of Leyland, who did not want to be named, told the Leicester Mercury newspaper: "Somebody took a photo of her ... and then she was gone. I haven't seen her since."
Another resident said: "While I wouldn't condone what Brenda is accused of doing, I am worried for her safety now she has fled."
A Leicestershire police spokeswoman said: "Police were called ... to reports of a body of a woman in a hotel room in Smith Way, Grove Park. Officers have attended the scene and a file is being prepared for the coroner. Identification of the deceased is a matter for the coroner. The death is not being treated as suspicious."
On Facebook, her son Ben Leyland, who lives in Los Angeles, wrote: "I love you, mum, and I will miss you forever."
Leyland was educated at a convent school and studied at Goldsmiths, University of London.
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Burton Overy is just 24km from the McCanns' home.
An 80-page dossier containing hundreds of tweets, Facebook posts and messages posted on online forums was handed to the Metropolitan Police by members of the public sickened by the abuse in recent months. The trolls believe the McCanns were involved in their daughter's disappearance.
Many posts suggested that the McCanns should be tortured and killed. Madeleine's younger siblings, 9-year-old twins Sean and Amelie, have also been subjected to threats. Among the many comments attributed to Leyland on Twitter was one that said: "Q 'how long must the Mccanns suffer' answer 'for the rest of their miserable lives'."
Gerry McCann told BBC Radio 4's Today programme that, while he had not seen the @sweepyface tweets, online abuse had caused his family "severe distress".
"I think we probably need more people to be charged," he said.
"We do not have any significant presence on social media or online. I've got grave concerns about our children as they grow up and start to access the internet in an unsupervised capacity."
During a Twitter discussion session about the online abuse suffered by the McCanns, Brunt was criticised by some for identifying Leyland.
Brunt responded that Sky News had done so through "normal journalistic and legal methods" and denied he had "stalked" or "chased" her.
- Independent, Telegraph Group Ltd, Daily Mail