There is no specific legal requirement for a cosmetic product to be declared as Kosher.
Kosher is generally used in reference with food, but there is a growing market for cosmetic products to be "Kosher". Central to Kosher food is the separation of meat from milk. The prohibitions against mixing them are very strict. Foods that are neither meat nor dairy are called pareve. The Kosher food labelling system identifies whether it contains dairy or meat ingredients. It would be expected that cosmetic products claiming to be 'Kosher' are prepared according to these values. Some organisations offer certification for Kosher products.
All claims should be true and not misleading according to the Consumer Protection from Unfair Trading Regulations 2008.
It is likely that such brands and products will be labelled as Kosher and are usually easily identified by searching 'Kosher cosmetics' on the internet.