Where do you staaaaaaaaart..... ugh.
Magic a system whereby we have enough police and local authority funding to enforce any legislation...
Deal with the huge issue we have with poverty, drugs, education, minorities feeling oppressed/repressed/hard done to, (i dont know how, magic wand?!)
Dog specific:
Breeders to be responsible for dogs they produce, for the life of the dog. SO if that dog is involved in an incident, potentially (not automatically... but potentially) the breeder is also liable.
Breeders to be traceable at any point in a dogs life - both breeders AND buyers to be responsible for that. So if you own a dog that has no chip, or you 'forgot' who bred it or 'can't remember' where you got it...
Chain of ownership responsibility - buy a dog, pass it on, still retain some responsiblity for where that dog went and what it does.
So owners would need to keep details of training, insurance, vet records - the more info and data they have proving they are/were a responsible owner, the less likely it is they could be liable.
We probably need some sort of exemption scheme - this all applies to dogs over 20kg or dogs over x height and x weight.
Mandatory third party insurance for dogs over x height/weight...
I think a carrot/stick scheme might help too - if you can prove your dog attended a suitable training class or you've taken a suitable dog ownership course, then your third party insurance is cheaper than if you haven't.
We REALLY need to crack down on those training dogs using abusive aversive methods - we have the science that shows us dogs trained this way are more likely to be dangerously aggressive, more likely to be unpredictable.
Ditto those training dogs to be aggressive on purpose - VERY few organisations need dogs trained to bring down people. This should not (sorry for those who do do this responsibly) a sport or hobby for pet dog owners, accessible to anyone who can watch a few videos and enter a competition.
Super strict licencing for dogs trained to do off-lead security/protection work - the current system for that is rubbish.
Increase the education on dog behaviour, how to source a dog responsibly as well - a quick trundle through Mumsnet shows that dog related knowledge is poor.
But it all needs the people and the money to police it - and we have not got that.