While technically there are other types of rock present, they are not as significant or widespread as the chalk:

1. Chalk: This is the dominant rock type, forming the iconic white cliffs and rolling hills. It's made from the tiny skeletons of marine organisms called coccolithophores.

2. Clay: Found in pockets and underlying the chalk in some areas, clay is another sedimentary rock formed from the deposition of fine sediment.

3. Flint: This is a hard, dark rock found within the chalk. It forms as silica in the chalk hardens and crystallizes.

Therefore, while you could say there are multiple types of rock, the South Downs are primarily characterized by chalk, with lesser amounts of clay and flint.