Tile grout, especially in wet and damp areas such as showers and around baths does tend to discolour after a period of time and if left alone will eventually turn black and become very unsightly.
I have the same problem in my own bathroom but rather than re-grout the tiles (one of my top three don’t want to do it jobs) I tried a grout pen which basically colours the grout white.
The discoloured grout should be cleaned as much as possible, I used an old toothbrush and liquid soap with hot water, this takes quite a while but it did remove some of the grout discolouration, then rinsed off the tiles and grout with clean water.
Dry the tiles and grout with a towel or cloth and wait several hours or more if possible so the grout is completely dry.
Safety Tip :- If you decide to use cleaning agents wear gloves, avoid splashes and keep the room well ventilated.
When you are confident the grout is dry (read the instructions first) run the grout reviver pen along each of the grout lines you want to whiten, depending on how badly discoloured the grout is, you may have to repeat this along the grout lines to achieve the desired result.
To prolong the life and colour of both tile grout and sealant it is worth trying to get everyone who has a shower or bath just to spend a minute or two drying off the tiles and around the bath or shower base with a dry towel when they have finished, doing this will reduce any mold growth and therefore reduce the discolouration. If, like me you have teenagers at home who leave the bathroom looking like a water park this might take some persistence on your part.
Tools required:- Liquid soap/sugar soap, old toothbrush or small stiff brush, dry cloth or towel and a lot of elbow grease and patience, grout reviver pen.