Firstly, make your own solution to tackle shower residue, consisting of equal amounts vinegar and water. It is best to mix these together in a spray bottle for ease of use, then add a single tablespoon of dish detergent.
Then, spray the solution onto the soap scum, leaving it to work its magic for around 15 minutes or so.
After this, scrub the surface with a soft-bristle scrub brush, and rinse away with hot water. Dry thoroughly for the best results possible.