Tessa Lake, 35, from Swindon, was out shopping with her three-month-old daughter Arya when she went into one of the brand's branches to ask for some water to warm a bottle.
However, staff said they could not give her the water as a matter of health and safety.
She complained to Costa, who said that this was not their policy and that they would reiterate their guidelines to staff - but Tessa has since been to three further stores and had the same experience each time.
'To begin with I only emailed their head office to complain because I was a bit cross about it and then it became a bit of a sticking point for me that they hadn't sorted it,' she said.
'They refused to give me hot water on health and safety grounds but will happily sell piping hot drinks which is just ridiculous.'
'They kept saying it over and over and so it seems to them that apparently a cup of tea is not a health and safety risk yet a cup of hot water is.'
'Costa is probably one of the coffee shops that a lot of parents go to to catch up with other mums which is why it makes their actions even stranger,' Tessa added.
'When you are bottle feeding, sometimes it is more difficult than breast feeding because you need to think of somewhere you can get hot water and you rely on that amenity.'
'For such a big name like Costa to not follow the request it is quite something, especially when other coffee shops like Starbucks are happy to accommodate.'
The brand have issued a response to Tessa's complaint, apologising for her experiences and confirming that they welcome both breast and bottle feeding mothers into their branches.
'We are renowned for our family friendly environment and our coffee shops are the perfect place for mum’s to relax with their children,' they stated.
'We welcome mothers to breastfeed in store, warm bottles and deliver drinks to their tables.'
'We have apologised to the customer for her experiences and will be reissuing communication to teams to inform them of our family friendly policies.'