Superdrug does state if its vegan.
The bunny logo is a logo used by independant campaigners BUAV (British Union for the Abolition of Vivisection) and they review companies who produce cosmetics and household cleaners to approve them as truely Cruelty Free (meaning neither the finished product nor the ingredients indivually were tested on animals)
Some companies can techincally claim they 'dont test on animals' because the finished product wasnt, but parts of it may have been. Thats where the BUAV come in to make sure all is above board.
They explain it better on their websiteswww.buav.orgwww.gocrueltyfree.org
Personally I dont use anything unless its been BUAV approved, some are ok trusting the 'we dont test on animals' claims by brand names. Its really down to what you want to do. Hope this helps.