The criminal law already addresses the issue. Dog owners must by law have our dogs ‘under control’ in public places. It’s a criminal offence to allow our dog to be ‘dangerously out of control’, either in public or private (such as inside someone's home). A dog is deemed dangerously out of control for this purpose not just if it physically hurts a person or another animal, but if someone feels at risk of being injured by the dog.
Being under control, and being on lead, are totally different things, so mandating leads doesn't fix the problem of individual non-compliance with the present law.
An off lead GSD or mastiff can be under perfect control, and recall or stop and wait instantly on cue. An on-lead pug or cockapoo can be a complete menace. It's not about the presence or absence of a lead.
The recent tragic death of the dog walker reportedly happened while the dogs were being walked on lead.
And most injuries in the stats happen in the home.
My cocker spaniel is currently on a lead or longline in public places at all times, unless he's practising a long retrieve or similar, because he is an adolescent over-friendly k**bhead atm who's still learning impulse control so I can't guarantee he won't become selectively deaf if he sees another dog he wants to play with or a pigeon he thinks he should be chasing. But my long term aim is to be able to have him off lead in situations where we currently use a longline.
And exempting "working dogs" wouldn't help most people. Most working breed dogs aren't owned by professionals. Mine is a working breed and a pet, who does gundog training on dummies to give him a "job". He would have a miserable, frustrated and confined existence if I had to restrict him to on-lead walks only, and would I'm sure end up pretty neurotic, and probably on meds for his resulting behaviour/mental health issues. Do we really think it's proportionate to have all the spaniels, cockapoos (those cute wee teddy bears are gundog breeds on both sides...), labradors, goldies, collies etc confined to 2m leads for life unless they are owned by professionals who work them professionally, or by the very few lucky privileged people with their own broad acres of private land?