Regardless of the material of your rims, Kool Stop salmon brake-pads will improve your braking by leaps and bounds than most others. Seeing you are in England, you might find equivalent performance from SwissStop pads for less money. Check about.
Cheap pads that come stock on bikes do tend to disintegrate in short order. If a Kool Stop or SS does that - you don't have steel OR alloy rims - someone rolled an angry crocodile into a circle and shoved spokes into him. ~~~*<