The Government had been planning to change rules which mean large stores in England and Wales can only open for six hours.
But it was being opposed by the SNP.
A Christian campaigner has told Premier that the government was right to be concerned if the Scottish National Party (SNP) votes against proposals to relax Sunday trading hours.
It is thought that SNP MPs were planning vote against the proposals in the House of Commons due to concern it could drive down the wages of people in Scotland who are currently paid more to work on a Sunday.
David Lawrence from the Christian campaign, Keep Sunday Special, was speaking before the announcement and told Premier's News Hour: "The government assumes that perhaps in an increasingly secular society, people no longer value their shared sense of rest.
"But we want to persuade MPs that this is not the case."
Speaking to the BBC, Angus Robertson, the SNP's Westminster leader said he welcomed the government's "U-turn".
He told BBC reporters his party supported Sunday trading but not "on the back of often lower-paid shop staff".
Number ten said there had been "absolutely" no U-turn on the idea.
On it's website on Tuesday the SNP party stated: "The SNP will take every opportunity to oppose the bill – including voting against it this evening."
The SNP would have potentially joined with Labour MPs and around 20 rebel Conservative MPs to block the changes.
Earlier in 2015 the Chancellor, George Osborne, outlined proposals in the Budget that would devolve powers to set Sunday trading rules to local councils and mayors.
At present larger stores, like supermarkets, are only allowed to open for six hours on a Sunday.
David Lawrence said: "The government have been really silent on this, but they really should be concerned about an opposition. I think they will probably try to head off the rebellion, but I think they underestimated how much their own MPs as well as many others from different parties care about this issue."
Angus Robertson, the SNP's Westminster leader, commented: "SNP MPs could hold the balance of power in the House of Commons on Sunday shopping and we will not undermine shop workers.
"This legislation will impact on workers in Scotland and elsewhere in the UK and no pay safeguards have been offered by the Westminster government.
"The SNP will continue to work with the representatives of shop workers and we will oppose the Tory proposals."
Now ministers are thought to be looking at changing the idea - or even dropping it.
Listen to Premier's Marcus Jones speak to David Lawrence from Keep Sunday Special here:
