Scientists at Imperial College, London, recently found that pugs in the UK are so inbred that although there are 10,000 of them, it is the equivalent of just 50 distinct individuals.
Steve Jones, professor of genetics at University College London, said: "People are carrying out breeding which would be first of all entirely illegal in humans and secondly is absolutely insane from the point of view of the health of the animals.
"In some breeds they are paying a terrible price in genetic disease."
RSPCA chief vet Mark Evans was interviewed for the programme.
He said: "The welfare and quality of life of many pedigree dogs is seriously compromised by established breeding practices for appearance, driven primarily by the rules and requirements of competitive dog showing and pedigree dog registration."
The Kennel Club's Bill Lambert and RSPCA chief vet Mark Evans
But Kennel Club spokeswoman Caroline Kisko said it is "working tirelessly" to help improve the health of pedigree dogs.
"Any dog may be shown but it is up to the judge to decide if it fits the breed standard," she said.
"It is when characteristics become exaggerated that health problems can occur.
"This is something that the Kennel Club does not encourage and actively educates people, including judges, against doing as part of its Fit For Function, Fit For Life campaign."
Pedigree Dogs Exposed will be shown on BBC One at 2100 BST on Tuesday 19 August
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.