Yes, the country of origin is required on cosmetics in the UK. According to the UK government’s guidance on making cosmetic products available to consumers in Great Britain, the label for cosmetic products must include the country of origin if the product is imported to the UK The information must be given on both the container and the outer packaging, and it must be written clearly and indelibly in English. Additionally, the name and address of the Responsible Person based in the UK must appear on the label of cosmetic products sold in the United Kingdom.
The law applies to EU countries as countries, so you have to put say, France, rather than the European Union.
The relevant section is Article 19.