Thanks for these! Will try bicarb first and bleach if that doesn't work. I have seen those grout whiteners but I don't want to just paint over the dirt
When we redecorate in 10 years' time I'm getting darker tiles and dark grout .

Nuclear option.

If you are really desperate, lock everyone out of the kitchen, and pour runny bleach over the grout and leave it. Don't use thick stuff it will be very foamy to mop up. Wash floor later. All grout will be lovely and white.

Try testing a patch first

etc

Bicarb soda, make a paste up with water and use your toothbrush. It's a pain in the a but it truly works. ( I got the tip from another mumsnetter)

You can get a grout whitener product which we have used in the bathroom, like a sort of pen and you paint it on. Not sure if it comes in different colours though (bought from BnQ). Or you could regrout it lightly in a darker colour so you don't have to clean it constantly!!!

When we moved in to our house 18 months ago we had lovely cream grout between the kitchen floor tiles. Now it is a horrid brown/grey colour. How best to clean it?

Who would put cream grout on a kitchen floor anyway? Only a male builder trying to sell his shiny new house...mutter mutter.