The Rt Revd Nick Baines, the acting Bishop of Leeds, said labeling "is essential" so people know what they are eating.
While the new Bishop of Liverpool, Rt Revd Paul Bayes, believes more "room" should be made for people of faith who face "implications" over what they consume.
The bishops' position has been echoed by Muslim and Jewish faith leaders who have written an open letter on the issue in the wake of the revelations.
The Muslim Council of Britain and Henry Grunwald, chairman of Shechita UK, which represents the Jewish method of religious slaughter, have called on faith communities to support comprehensive labelling.
They wrote: "Consumers should be informed whether an animal has been mechanically stunned before being slaughtered and whether it has endured repeat stuns if the first attempt was ineffective.
"They should also be told the method of slaughter: captive bolt shooting, gassing, electrocution, drowning, trapping, clubbing or any of the other approved methods."
Alison Ruoff's a lay member of the General Synod of the Church of England and long-time campaigner for halal labeling. She told Premier why she wants new rules introduced.
Pizza Express is one of the restaurants accused of failing to inform customers. The company denies the claims saying the information is available on the customer service section of their website.
The company, however, did say that it is "looking at whether we take steps to make this information even clearer" through its menus.
The National Secular Society has also called on the government to bring UK animal slaughter laws into line with the rest of the EU.
A spokesman said: "Food retailers should be upfront about what they're serving up, but surely the main issue surrounding halal and kosher meat is one of animal welfare, and the religious exemption from UK law that allows animals to be slaughtered without first being stunned."
The Department for the Environment, Food and Rural Affairs has said the UK government has no intention of banning religious slaughter.