One measure that could be taken would be to ban the sale and rehoming of dogs (and all animals) on selling sites such as Gumtree, Pets4Homes, Preloved, etc. Animals should only be available from approved sources such as registered breeders, rescues, or rehoming services. So many dogs re passed from home to home with no consideration about whether they're suitable for their new home/owners, what their past history is, and their welfare.
To help enforce it there should be a system whereby the public can report unauthorised sales/rehoming and can report concerns about dogs that are aggressive. Local authorities and police should have powers to seize such dogs, assess them, and then either issue a penalty (e.g., a fine), destroy the animal, rehome somewhere more suitable, or return it to the owners.
This could be funded by a license fee for dog ownership and the (hefty) fines collected. Yes, dishonest owners just wouldn't get a license but thats life, no measure will have 100% compliance, however actually enforcing regulations would deter a lot of them and it would reduce the numbers.