I'll tell you what I have found useful for cleaning grout, THESE LITTLE WIRE BRUSHES I didn't get them from amazon though, I think they were £1 in Home bargains
I needed my tiles re-grouting and decided to buy 2 grouting pens from Wilko the offer was buy 1 get 1 half price I wish I had never bothered it was rubbish I ended up getting DGS4 to re-grout the whole area in fresh grout
I can confirm ever build grout restorer in a squeeze tube works. Quick to apply with your finger, slightly messy but gives a very bright white finish. I've done half of mine so far. Previous occupiers smoked heavy and never cleaned anything in years, everything was an orange/brown colour. Now the tile grout looks brand new. I must finish the rest in the shower!
I'm sure the one I used put a kind of plastic coating on the grout which soon peeled off. That was many years ago, perhaps they've improved since then.
Ever build forever white grout reviver is brilliant! Under £5 a tube. Just clean the grout and tiles, I used my finger to apply, once dry clean excess from tiles. I needed to smarten up a bathroom in a house I was selling, the tenant never cleaned the bathroom thoroughly and the grout had gone a rusty colour in places. It looked as good as new when I had finished! Amazon sell it.
I carefully painted some old grout with white masonry paint. I wiped it off the tiles as I went - worked really well.
Be very careful with tile paint, though, Grannynannywanny. I'm sure that you have to clean and prepare thoroughly first. My daughter once lived in a flat where the bathroom tiles had been painted - and it was flaking off.
I have also cleaned grout in the shower tiles using powdered Ajax mixed to a paste and applied with a sponge to the whole area - leave for 20 mins or more and then wash off with the hand shower head - mine came up a treat.