It’s all very well saying bring back licences etc etc etc it the reality is that that is unenforceable when anyone can pick up a dog on gumtree or down the pub.
You start by banning the profiting from sale of animals, any animals. That means you shut down the puppy farming industry overnight, since the only reason these puppy farms exist is to make money.
You then shut down Pets4Homes, and any other sight is banned from advertising the sale of animals unless it’s a proper breeding sight.
No-one is going to then be breeding their animals for the purposes of making money because it will be common knowledge that buying a dog for £1000 upwards is unnecessary when that person is selling their dog illegally and you can go to a more reputable breeder.
You ban the import of animals including the import of rescues into the country. Most of them are unsuitable for rehoming as they haven’t been socialised and there are no end of problems with them. We have enough unwanted rescues in this country without bringing in more.
All dogs in rescue need to be subject to inspection by a professional. If a dog is deemed unsuitable for rehoming then it needs to be destroyed. No dog should be passed from home to home, and no dog should be left languishing in kennels for the rest of its life. A humane end is far better for the dog than any of that.
It’s not the decent owners who need to be penalised. There’s no need to ban dogs off leads, dogs need exercise and a dog which gets no exercise is more likely to become aggressive or destructive, and most dogs are well behaved. But clamp down on the availability of untrainable dogs with often questionable health records due to the fact they’ve been bred for money and nothing else, and you go a long way to solving the problem.