Its chairwoman, Dr Judy MacArthur Clark, says that animals suffer significantly unless they are stunned - a position backed by animal welfare charity the RSPCA.
Both kosher and halal butchers have reacted angrily, arguing that their methods are humane and actually cause less suffering to animals.
Dr MacArthur Clark said there is absolutely no doubt that stunning will always make the slaughter process more humane.
Muslim Council of Britain
She said: "The rendering of unconsciousness is a very immediate thing that happens, therefore those animals are clearly suffering far far less because the period of time over which they suffer is extremely short."
She said under the halal and kosher systems adult cattle can take up to 40 seconds to lose consciousness, while calves can take two minutes.
"Those are very significantly long periods of time for the animal to be suffering before it loses consciousness," she said.
One rabbi who had been practicing the Jewish method of animal slaughter for around 40 years told BBC News it was humane.
He said: "The process takes a fraction of a second.
"With a very, very sharp knife all the vessels in the neck are severed and that means there's no blood going to the brain and the animal loses consciousness very rapidly and dies soon after that."
The Muslim Council of Britain says stunning is forbidden on religious grounds and that studies show it is actually more harmful to the animals.
A spokesman said: "We oppose it from a legal point, from a religious point, from a health and medical point and from an animal welfare point."
The Farm Animal Welfare Council has previously recommended that the exemption on religious slaughter be removed.
But on that occasion, in the 1980s, it was ignored.
The government will receive the council's report in June.
It says it will take careful note of any religious sensitivities before deciding what to do.