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.
He said he shared “the nation’s horror” over videos of recent dog attacks and had ordered urgent work to define “and ban this breed so we can end these violent attacks and keep people safe.”
It comes after a 52-year-old man died in Stonnall, Staffordshire after being attacked by two suspected American bullies on Thursday afternoon.
Father of two Ian Price suffered fatal injuries after the dogs escaped from a nearby property. Neighbours say Mr Price was outside his elderly mother’s home when the attack occurred.
“My daughter heard screaming and barking and came running out to see what was happening,” one neighbour told the Mirror. “One of the dogs, a white one, was covered in blood and wagging its tail. She said it was a horrific sight.”
Even before the ban is introduced, home secretary Suella Braverman said she expects police to “use all available powers to protect the public from these beasts”.
The move was backed by campaign groups, Labour, and the architect of the Dangerous Dogs Act more than 30 years ago, Kenneth Baker.
Mr Sunak said it was now clear that the problem was not “about a handful of badly trained dogs” but “a pattern of behaviour and it cannot go on”.
“While owners already have a responsibility to keep their dogs under control, I want to reassure people that we are urgently working on ways to stop these attacks and protect the public,” he added.
But he admitted that a ban would take time as there is currently no definition of the breed, which are larger versions of American pit bulls. Police and other experts have been tasked with solving that problem, to allow ministers to ban the animals under the Dangerous Dogs Act by the end of the year.
A series of attacks have recently hit the headlines, with an 11-year-old girl left with serious injuries in Birmingham last week, and two other men also injured.
After footage of the dog clamping its jaw around her arm went viral, schoolgirl Ana Paun said that “all of the dogs... all of them should be banned”.
Last weekend Ms Braverman also backed calls to ban the breed and announced she would be commissioning “urgent advice”.
Lord Baker said bully dogs should be “neutered or destroyed” once the ban has come into force, with any permitted to live being “muzzled for the entire time”.
Speaking to LBC, the Tory peer said: “It should be done almost immediately because this is a very dangerous breed and it has actually killed children and attacked other people, and I do not accept the views of the Kennel Club and the RSPCA that breeds should not be banned.
“This dog is, in fact, bred in order to fight and to be aggressive. It has already done enough damage and the prime minister is absolutely right to add it.”
Campaign group Bully Watch said the breed was a “a clear and present threat to public health”.
While Labour supported the ban it criticised the prime minister for “dithering” over restrictions on ownership.
Shadow environment secretary Steve Reed said: “Families will be furious that it has taken this long for Rishi Sunak to finally act.”
But a coalition of animal charities, including the RSPCA and the Kennel Club, said banning the dogs would not stop attacks.
A spokesperson for the Dog Control Coalition said: “For 32 years, the Dangerous Dogs Act has focused on banning types of dog and yet [that] has coincided with an increase in dog bites. And the recent deaths show that this approach isn’t working.
“The UK government must tackle the root issue by dealing with the unscrupulous breeders who are putting profit before welfare, and the irresponsible owners whose dogs are dangerously out of control.”
The group, which also includes the Dogs Trust and British Veterinary Association, said it was “deeply concerned about the lack of data behind this decision and its potential to prevent dog bites”.
In Thursday’s fatal attack, Mr Price was mauled to death by two suspected XL bullies in Main Street, Stonnall, with police forced to lock down a nearby primary school.
He was found with “multiple life-threatening injuries” and died in hospital later. Staffordshire Police have since confirmed that both dogs have died – one while being restrained after the incident and another by lethal injection.
A custody extension has now been granted giving detectives another 10 hours to continue questioning a 30-year-old man from south Staffordshire in connection with the incident.
It has also emerged that police attended two previous incidents involving the dogs, in January and March. However, the force is not being investigated by the Independent Office for Police Conduct watchdog.
The UK does not currently recognise the American bully XL as a specific breed, although they are recognised in the US.
According to Bully Watch, the dogs first started to appear in the UK around 2014 and the breed saw a rapid increase in popularity during the pandemic.
In the past five years, there has been a 34 per cent increase in dog attacks, from 16,394 in 2018 to 21,918 last year.
There were 10 fatal attacks in 2022, six of which involved an American XL bully.
However, experts and animal charities including the RSPCA and British Veterinary Association have warned that breed-specific bans are ineffective and could see thousands of innocent dogs put down.
Leading veterinarian Dave Martin told The Independent: “We tried that with pit bulls and it didn’t work at all. We need to be looking at a multifaceted approach to reducing these attacks.”
He added: “If we ban these dogs tomorrow, what are we doing with the thousands of bully XLs that are already wandering around our streets? Are we suggesting that we put them all to sleep, which would just be something I can’t see the public ever agreeing to.
“Or are we going to have some sort of licensing system for those dogs? In which case we need to see the details to know whether that’s actually going to have any effect whatsoever on reducing the level of injury or death that these dogs are causing.”
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