It is worth knowing that Simple a big brand of skin care products offer a large range that contain no animal derived ingredients.
I have over the years tried a few different types from the face cream to hand cream. They do hand wash and everything you could imagine including anti wrinkle cream.
Sometimes I use their body wash/shower gel, they do a few different varieties, some are clear and some have a creamy texture. I find them quite pleasant to use and they do not seem to irritate my skin. They do not use heavy chemicals.
Always check the label and look for the “contains no animal derived ingredients” as some of their products are not OK for vegans.
Simple products are sold in supermarkets, chemists, Superdrug and most smaller grocery shops.