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!!!
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.
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 .