Here is a good resource for compounds which can be harmful, although they are more related to health rather than environmental concern.
That said, anything which is toxic to humans is likely toxic to other organisms, especially when concentrated and bioamplified. I'll summarize the environmental effects below:
The really common ones you hear bad things about are phthalates, sulfates, and parabens (many companies/products will promote the fact if they are free of these compounds)
Sodium laureth sulfate (a foaming agent) might contain 1,4-dioxane, which persists in the environment.
BHA (butylated hydroxyanisole) and BHT (butylated hydroxytoluene) used as preservatives in lipsticks and moisturizers, among other cosmetics and food preservatives. They are toxic to aquatic organisms.
Coal tar-derived colours and P-phenylenediamine (classified as toxic in the EU) are also toxic to aquatic organisms and environments
Also toxic to aquatics:
DEA (diethanolamine), Dibutyl phthalate (DBP), and triclosane.
Plastic "micro-beads" are also really bad because water treatment facilities do not filter them out and they can be eaten by fish, etc., and may break down to other harmful things as plastic does. They are currently being phased out in Canada, though I don't know if the UK has already done this.