But unions and religious leaders have criticised the proposals, which they fear will further undermine family life.
Details of the plan were finally confirmed by chancellor George Osborne in Wednesday’s Budget.
Afterwards, borough council leader Nick Daubney said: “We very much welcome the chancellor’s initiative and wholeheartedly support his efforts to encourage growth.
“We understand that there will be implications locally. We therefore think that being able to make local decisions about Sunday trading, having spoken with the town centre partnership and other retailers, will result in the best outcome.”
But Linda Cox, joint secretary of the Lynn and District Trades Council, fears employees may lose out from such a move.
She said: “Shop workers are notoriously low paid and extended hours will have extra costs, such as childcare or public transport, which will be more expensive and difficult to obtain on a Sunday.
“This will further exploit workers by impacting on their right to a work-life balance and lead to workers being expected to be available for work seven days a week. Sunday is often the only day families get to spend quality time together.”
The Bishop of Lynn, the Rt Revd Jonathan Meyrick, felt councils would be limited by neighbouring authorities’ actions to relax the rules.
But, while he recognised shopping was an important leisure activity for many people, he is worried that allowing additional trading time on a Sunday will make it increasingly similar to any other day of the week.
He added: “I hope people don’t lose sight of the fact that to have a regular period in the rhythm of one’s life that encourages rest and recreation is a very good thing.”
Under the current regulations, larger stores are only allowed to open for a maximum of six consecutive hours on a Sunday.
However, the rules were relaxed on a trial basis for seven weeks in the summer of 2012, coinciding with the period in which London staged the Olympic and Paralympic Games.
But opponents argue the evidence of that experiment does not warrant further relaxation of the law.