He added: "Puppies and kittens are housed and sold without their mothers and the presence of such retail outlets encourages impulsive buying, irresponsible breeding, and commoditisation of these animals, as well as too often leaving prospective owners with the burden of life-threatening health and behavioural problems associated with pet shop puppies."
Mr Flello said there needed to be better public information to encourage people to only buy puppies and kittens when their mother was present.
Labour's shadow environment minister Angela Smith warned that irresponsible breeding of cats and dogs was "only the tip of the iceberg", highlighting welfare concerns about the "growing" trade in online sales.
Conservative minister George Eustice, concluded the debate saying a new voluntary code of conduct for pet sales in operation since the start of the year has resulted in 100,000 adverts from backstreet breeders being removed from the internet.
In addition, he said, puppies would not be allowed to be legally imported into Britain unless they were at least 15 weeks old, under EU rules.
He said pet shops were licensed and regulated under the 1951 Pets and Animals Act - but there was "much that can be done" to strengthen the regulations to improve animal welfare.
He promised that further guidance would be issued to local authorities to provide clarity on enforcement of rules.