Banning breeds has worked for the pitbull. I work with dogs and I’d never even seen one for years never mind heard of a mauling by one (thankfully). We now need to make it illegal to own a dog descended from, related to or created from a banned breed to avoid this mess happening again.
It didn't work, though. You only need to look at the list of fatal dog attacks to see that.
Pitbulls were "banned" in 1991 yet they were involved in fatal attacks in 1993, 2007, 2009, 2012, 2013, 2014 (twice), 2015 and 2016 (twice).
https://en.wikipedia.org/wiki/List_of_fatal_dog_attacks_in_the_United_Kingdom
In fact, in 2007, nearly 200 illegal Pitbulls were handed over to the police after a 5yo was killed by one (receiving 72 injuries in total).
Banning breeds doesn't stop those breeds existing, it doesn't stop dogs from attacking and it doesn't stop people from mixing together other breeds to create more, equally dangerous dogs.