Rachel Williams' son, Jacob, is allergic to peanuts, hazelnuts and almonds.
"It is difficult enough to navigate life with allergies without adding the learning of Latin on top of everything else," said Rachel, from Swansea.
"I can't always remember the name of certain nuts in Latin, or I doubt myself when I'm checking products. This means I have to search online every time I use a product. I would have a lot more confidence in the products if they stated all of the top 14 allergens in English."
The CTPA has defended the use of INCI ingredient names.
Caroline Rainsford, the director of science at the CTPA, said the system provided a universal language across the globe.
"For botanical or natural extracts, we refer to the Linnaean system, which is the international system for scientifically naming plants and animals, and lots of those names will be Latin-based," she said.
"The reason we refer to that system is to have global harmonisation.
"I can see that perhaps people would think it may be easier to have the English name but if you are on holiday and you are looking at the ingredients list, you would need to know the name of the plant in whichever country you're in.
"Whereas if we use the INCI system, you then just need to remember that one INCI name.
"The more consistency and harmonisation we have with the ingredient list is not only great for us when we're buying a product, it also makes life easier for companies."
The industry has developed tools to help consumers navigate the terminology.
One such tool is the COSMILE app, which allows users to search ingredient names by scanning the label.
The app aims to offer reliable and scientifically supported information on thousands of ingredients used in cosmetic products.
A UK government spokesperson said: "Our regulations require all cosmetics to include a full list of ingredients that is clearly marked on the product label or packaging using generally accepted names."