Its an American list. a British one would have other brands on it but the problem is the same. Also, as other posters have said, they haven’t put on the brands that we like to think are ethical. For example, Kraft also owns Green and Blacks.
Unless you are buying only from co ops and box schemes, odds are you are buying from these big companies. Lots of supermarkets have stuff made by these companies too and sell it as own brand.
My feeling is that its best to buy from worker-owned companies, but if we must buy from these big companies, choosing ethically still makes a difference because it sends a message that this is what we want.