The primary purpose of UV lights is to remove excess combined chlorine (CC), normally only an issue on indoor pools. Properly installed UV lights will help reduce algae but can't possibly eliminate algae on their own. Likewise they can provide some assistance in sanitizing the pool, but can never sanitize the pool on their own. UV lights only affect the water passing through them. The bulk of the water remains in the pool at any given moment and is thus not protected.
You have to have some sanitizer in the bulk pool water or the water is not safe to swim in. The only three EPA approved sanitizers are chlorine, bromine, and baquacil. Chlorine is usually the best choice. Bromine is good for hot tubs because it is more stable than chlorine at high temperatures. Baquacil is rather expensive and many people using baquacil report major problems after the first year or two.