Citric acid

coffeehound

I can strongly recommend trying a scraper.  I got a Harris decorators scraper that uses the standard trapezoidal stanley knife blades (might find one similar in a pound shop) and it instantly removes limescale and soap scum back to clear glass.  A very shallow angle of attack seems best.  It propably would not be usable where there are applied decals, decorations etc on the shower screen, though

Solarchaser

Citric acid is good for several applications. 
In industrial instrument reprocessing (scalpel etc for operations) citric acid is used specifically for limescale in many English hospitals. 

However living in Scotland I've no idea what limescale is 🤪