“We’re concerned that companies don’t compete strongly on price and many parents – who may be choosing infant formula in vulnerable circumstances and without clear information – opt for more expensive products, equating higher costs with better quality for their baby,” said CMA chief executive Sarah Cardell.

Just three companies – Danone, which makes Aptamil and Cow & Gate, and Nestle, which makes SMA, and Kendamil – control more than 90% of the UK market.

Prices for baby formula in the UK have jumped between 18% and 36%, depending on the brand, over the two years between December 2021 and December 2023, the report found.

Parents could make a saving of up to £500 over a baby’s first year of life by switching to a lower priced brand, the report found.

The market is currently regulated so that promotions, such as a loyalty points or discounts, are banned in the same way they are for tobacco and lottery tickets.

This is to encourage breastfeeding, which the NHS says is healthier for children, but the CMA said it was concerned this stopped firms competing on price, with an “unintended consequence” of this meaning “consumers paying higher prices”.

It said “permitting prices and price reductions to be publicised”, would encourage price competition.

It found there was “little pressure” on firms “to shelter customers from increases in manufacturing costs, which have largely been passed on quickly and in full”.

Despite these regulations, Asda started allowing loyalty points to be used to buy baby milk from January. Iceland has also spoken out against the rule.

The rules also require all brands of baby milk formula, including supermarket own brands, not to differ too much in terms of core ingredients.

However, the CMA is worried the words companies use to make their products stand out, such as “advanced”, make it hard to judge their quality.

It said this “risks diluting the important public health message that all infant formula meets nutritional needs” regardless of brand or product.