Say what you will about Anthea Turner, but her tip on cleaning floor tiles grout is no fail 100% positive result.
Mix bicarbonate of soda with a little bit of water to make a paste, apply and rub gently with a cloth. the dirt and staining comes off straight away!! And it does not require major effort at all.
I did my kitchen floor last night, ran out of bicarbonate of soda and sent DH out to buy me some more so I could finish. Amazing. It is as good as new now. I am soooo happy now!
Get cleaning ladies!