"Surely it is not unreasonable to suggest that, in the light of new scientific knowledge and society's more caring attitudes to animals, religious traditions might be changed," it added.
The booklet elicited condemnations from the Jewish Board of Deputies, the umbrella group representing secular Jewish organizations, and from the Federation of Synagogues and the London Shechitah Board.
A Board of Deputies official this week accused the animal rights group of "attacking religious rights" in the booklet, which has been sent to the group's branches and to its school liaison officers.
Board of Deputies president Eldred Tabachnik called for an early meeting with the animal welfare group.
"We will defend the religious and civil rights of our community, including the right to practice shechitah. Of course, we are right to be concerned over any manifestation of cruelty to animals. But there is no convincing scientific evidence that bears out the claim that shechitah is cruel," Tabachnik said.
The head of the group's farm animals department, Martin Potter, said his organization did not want a confrontation with the Jewish community.
"We want a constructive dialogue, and I am sad to think that the views in our booklet — which deals only briefly with religious methods of slaughter — are seen as a threat," Potter said.
He added that the animal rights group wanted a "modification" of shechitah, in which the animal could first be stunned.
He noted that portions of the local Islamic community had already agreed to this suggestion.