"The woman's probably off the planet. I don't think she's got any scientific credibility at all," Stuff.co.nz quoted Anderton, as saying.
The billboard, which started it all, shows the former model against a backdrop of burning farmland and the words: "You haven't got a leg to stand on."
The billboard reads: "So you're an environmentalist?" Not if you eat meat and dairy because livestock are destroying the Earth."
Anderton, who gave a speech on organic agriculture in New Zealand in August, said that he doubted the campaign would influence British public opinion, but admitted "it could have some effect."
"Let the facts get in the way of your ignorance and prejudices. Come and see a dairy farm in New Zealand and see what it looks like compared to what you're portraying," Anderton said.