Police were called out at 9am on Monday following reports of an incident inside a property in Belvedere, near Bexleyheath.
The Metropolitan Police said the woman was taken to hospital by paramedics where she remains in critical condition. A man involved in the attack was also taken to hospital for treatment.
The force said the dog - who was injured during the attack - was Tasered by police and later died while being held in a room by officers.
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A spokesperson for Metropolitan Police said: “Police were called at approximately 08:55hrs on Monday, 20 November to reports of a woman being attacked by a dog inside an address in Bedwell Road, Belvedere.
“Officers, London Ambulance Service and London’s Air Ambulance attended the scene – a woman, no further details – was taken to hospital for treatment; she remains there in a critical condition. A man also received minor injuries - he was taken to hospital for treatment.
“The dog received injuries during the attack and Taser was discharged by officers who secured it in a separate room. It has since died. Enquiries into the circumstances continue.”
A London Ambulance Service spokesperson said they attended the scene and dispatched London’s Air Ambulance.
“We sent a number of resources to the scene, including an ambulance crew, an incident response officer and members of our tactical response unit. We also dispatched London’s Air Ambulance,” a spokesperson said.
“We treated two patients at the scene before taking them to a major trauma centre as a priority.”
The incident is the latest in a string of dog attacks – some of them fatal – to have taken place across the country in recent months.
On Saturday, two people were airlifted to hospital after a dog attack in North Wales, where 37 other dogs were seized from the address.
XL Bully dogs have been involved in a significant number of recent dog attacks.
In October, a school was forced to evacuate in Norfolk after a 60-year-old woman was mauled by her pet XL Bully at her home, before it escaped from the back garden.
Rishi Sunak has announced the dogs will be banned by the end of the year following a spate of horrific attacks.
The prime minister said the animals, which campaigners have linked to at least 14 human deaths since 2021, are a danger to children and communities, in a video posted to social media.
Under the new rules coming into place on 31 December, American bully XL will be added to the list of prohibited dogs under the Dangerous Dogs Act. It will first be illegal to sell or breed the type of dog, before ownership will be outlawed in February 2024.