Some animals can be left so unwell they have to be put down.
Matt remembers one dog from Romania who arrived "barely responsive" after smugglers had tried several different ways of bringing it into the UK.
"It had a nappy on it to absorb urine and faeces. One of its legs was bandaged up so when it got on the veterinary treatment table, it was a raw stump. The vet said it was suffering beyond imagination."
Illegally imported dogs may also not have been tested for diseases like rabies or brucella canis, which can put animals in the UK, and their owners, at risk.
The new law will raise the age limit for importing puppies and kittens into Great Britain to six months.
The Animal and Plant Health Agency says that will make it easier to identify underage animals and will put a "blocker" on the trade because older puppies are simply less cute.
Some support the principle of the new age limit, but warn it could have unintended consequences.
Rosemary Kind chairs the Entelbucher Mountain Dog Club of Great Britain, and says they need to bring puppies into the country because "the gene pool is so small" that if they only bred from those here they risked introducing "health conditions that we'd rather not have in the breed".
She said waiting until a puppy was six months old to import would push up the cost significantly and wasn't practical.
"These are not puppy farms that we're getting dogs from. They're people who bring up dogs in their own homes. It's a big ask to ask them to keep the dog for that length of time"
She said other methods, such as bringing in stud dogs or importing semen were either impractical or carried more health risks, and she is working with The Kennel Club to call for exemptions for specialist breed puppies.