Parliamentarians are being urged to back a proposal that could help further reduce the cost of baby formula.
Iceland supermarket boss Richard Walker is calling for retailers to be given more freedom to help make first infant formula milk more affordable for families.
He wants lawmakers to amend a bill which is currently passing through the House of Lords to allow the secretary of state to make regulations regarding the promotion and sale of infant formula. Until now that has been under EU law.
Mr Walker believes it could allow shops to promote discounted infant formula and sell the product in exchange for vouchers or loyalty points.
He said: "We promised customers we wouldn't rest until we fixed this broken market and we have been working with legal experts to produce an amendment which we believe uses our separation from the EU regulatory framework to help hard-pressed families.
The Iceland boss is calling for cross-party support for the proposed change to the Digital Markets, Competition and Consumers Bill which is currently being examined in parliament.
"This amendment would give ministers the chance to strip away regulations which are currently making it harder for families to access more affordable formula," he said.
"While breastfeeding is always best for babies, the millions who rely on formula are struggling with costs and we believe this amendment would be a big step forward in the campaign to support them."
In December, the Competition and Markets Authority announced it was putting the baby formula market under further investigation after finding manufacturers were hiking prices higher than production costs.
Prices of baby formula have risen by 25% in two years.
The move follows a Sky News investigation last year in which parents revealed the desperate measures they were taking to feed their babies because they simply couldn't afford the prices in the shops.
Mounting pressure also led to one of the two market leaders, Danone, announcing a cut to the price of its Aptamil brand by 7% earlier this month.
While broadly welcomed, campaigners pointed out it was far from the only solution needed.
Parents and charities have also called for the government to raise the value of Healthy Start vouchers which have not increased in value since 2021.
Mr Walker has now written to Business Secretary Kemi Badenoch to ask for her support to back the proposed amendment.
He added: "We can't just wait for the Competition and Markets Authority finally to act on price gouging in the formula market: families need our help now."
In response, Dr Vicky Sibson, director of the infant feeding group First Steps Nutrition Trust, told Sky News: "The regulations governing the marketing of formula milk are intended to protect all babies, however they are fed.
"Attempts to weaken these regulations are not a solution to formula company profiteering, or to improving access to infant formula for struggling families and may put the health of babies at risk.
"We are liaising with the Competition and Markets Authority to support their follow-up investigation," she added.
The CMA will report back on their baby formula investigation later this year.