More than 20 Conservative MPs were prepared to rally against the measure, put forward in July by George Osborne, the chancellor. The proposal was not in the Tory election manifesto.
Plans to hold the parliamentary vote next week have been dropped as discussion continues over the reforms. The proposals are still expected to reach the Commons as an amendment to the Cities and Local Government Devolution Bill.
Church groups and corner shop organisations are opposed to change.
Speaking on Sunday trading laws during Prime Ministers Questions on 21 October:
Susan Elan Jones MP (Labour) said: "Following an extensive public consultation, the government's retail sector champion, Kevin Hawkins, described our current Sunday trading laws as a workable compromise that most people seem satisfied with most of the time. Does the Prime Minister agree with him?"
Prime minister David Cameron said: "I don't agree. I think there is a strong case for change. But I think it's a change that we should allow local authorities to decide and that's why we'll be putting it in front of the House, in the Cities and Devolution Bill, the opportunity for that to happen.
"But let me just give the Honourable Lady in the House two examples of where I don't think the current situation works.
"You've got these restrictions on opening hours for many stores that families would like to shop in, and you have to go to these stores and you have to walk around for hours before you're actually allowed to buy anything.
"The second point I would make is that you can shop on Sunday. You can shop anywhere on Sunday. You can do it on the internet and I think it's time to modernise our approach to give families more choice and help create jobs at the same time."