The director of Peta, Elisa Allen, told Mike Graham and Rachel Johnson: "One hates to use the word "freaks", but that is what Crufts has become".
The breeding of certain kinds of dogs "just adds to this animal overpopulation crisis that we have found ourselves in".
PETA has claimed responsibility, saying their members were protesting against "extreme breeding".
He said: "There are measures in place to ensure that the welfare of the greyhound is looked after all the way through their career".
Tease, a Whippet from Scotland, won the top prize at Britain's Crufts dog show in Birmingham on Sunday.
Eyewitnesses said he was carrying a banner displaying the name of the animal rights group Peta (People for the Ethical Treatment of Animals).
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Owner Yvette Short, of Edinburgh, could be seen clutching the overall victor, a two-and-a-half-year-old whippet bitch called Tease, as the commotion unfolded and security guards appeared to run down the intruder at the NEC Birmingham.
She grabbed her two-year-old whippet - named Tease - as the duo burst into the ring amid loud boos from the audience.
The crowd broke into applause as the intruder was taken away.
Crufts and the NEC said security would be reviewed as "a matter of urgency".
In the footage, which was partly captured and aired on Channel 4's live Crufts broadcast, a male protestor holding a placard that read "Crufts canine eugenics", ran into the arena.
A Crufts spokesperson said the intruders "scared the dogs and put the safety of both dogs and people at risk in a hugely irresponsible way".