Logical Harmony and Cruelty Free Kitty to check brands.
Decide what “cruelty-free” means for you e.g. Do you want to stick to products that have a certification only? Where do you stand on brands that don’t test products sold in Europe but do test “where required by law” (i.e. China)? Are you ok with brands that don’t test but are owned or part owned by parent companies that do test?
Content Beauty is a good retail website to look at, they indicate which products are certified cruelty-free. I’d second Naturissimo, but sadly they do stock brands which aren’t cruelty-free(e.g. Caudalie test in China and REN are owned by Unilever). Lovelula is another good retail site, but do check brands out as they sell REN (to be fair, they’ve sold REN since before they were bought by Unilever, and I would imagine it’s one of their central brands). Also Ecco-Verde for some stuff from Europe.
As for specific products.
So many cruelty-free brands are easily accessed only online, so I’ll start with things is relatively easy to find in a physical location. Barry M is good for nail varnishes, and also good because it’s so easily available, so if you need something in a hurry it’s easy to go and try it and get it. -Plumpy is a fab topcoat.. I also like Pixi for make-up and skincare as they have stands ina lot of M&S’s. Lipgloss is good, so are eyeliners, and the Retinol Tonic is brilliant. Herbivore is lovely and can be found in SpaceNK stores. They do a great range of cruelty free and vegan skincare. The charcoal soap is amazing, as is the blue clay mask. I like a little bit of Chantecaille make-up as an extra special treat, also at SpaceNK. Very pricey, but mascara is out of this world and illumination is gorgeous and lasts forever.
Otherwise, I like Evolue, Oskia, Dr Alkaitis, Alpha-H, Mad Hippie for skincare. Alba Botanical, Anadalou Naturals and Avalon Organics are all worth a punt. The Altruist is a great sunscreen. Pacifica do some lovely things too, especially make-up. Faith in Nature do great shampoos. Ere Perez do great eyeliners and lip stains.