A ban on puppy sales by pet shops and other third-party dealers in England is being considered by the government.
Under the proposals, people buying or adopting a dog would deal directly with a breeder or rehousing centre.
Environment Secretary Michael Gove said the plan would be examined as part of a new package of measures aimed at driving up welfare standards.
Enhanced licensing conditions for breeders are already due to come into force this year.
Under the new rules, breeders or sellers of dogs must be licensed and will not be able to sell puppies and kittens under eight weeks old.
Puppies must also be shown alongside their mother before a sale is made, and - amid concern over online sales - purchases must be completed in the presence of the new owner.
'Puppy trade crisis'
Last year, the Department for Environment, Food and Rural Affairs suggested a ban on third-party sales could lead to the creation of an illegal market.
But the Dogs Trust welcomed the government's latest thinking on the issue, which is subject to a consultation.
Paula Boyden, veterinary director for the Dogs Trust, said: "If a ban was introduced now, puppy farmers could exploit loopholes such as setting themselves up as unregulated re-homing centres or sanctuaries.
"Licensing and inspection of dog breeders and sellers must also be stronger to ensure that everyone involved in the trade is on the radar of local authorities."
RSPCA deputy chief executive Chris Wainwright said: "We have always said that an end to third party sales alone would not be enough to end the puppy trade crisis, and we are pleased that this is being looked at alongside enhanced licensing conditions for breeders."
The charity's chief inspector Ian Briggs said officers had found dogs and puppies "covered in filth" while kept in cold, damp pens with no light by breeders and dealers involved in the underground puppy trade.
He said: "We've also found tiny puppies kept in buckets amongst the dead bodies of their siblings."
The Mayhew Animal Home charity highlighted the case of Luna, a Jack Russell terrier who was sold online despite being ill with a suspected skin disease.
At six weeks old, Luna was already under the legal age required for puppies to be sold - but the seller claimed the young dog was 10 weeks old.
A Mayhew spokeswoman said the new rules, due to come into force at the end of October, will ban third-party sales like in Luna's case.
And Mayhew's chief executive Caroline Yates said: "Getting a dog or cat is not a commercial business and the big puppy farms have no regard for the health or welfare of animals.
"Owners are being duped into buying animals from these places."
In another case, the Dogs Trust said a French bulldog called Lola was forced to travel from eastern Europe so her puppies could be born and sold in the UK at a higher price. Two of her puppies later died.
"The law is not protecting these dogs and we need to be absolutely sure that future legislation is properly resourced and enforceable," the charity said.