Assuming they are stone tiles, spread Cola on them. Leave for 15 mins, then swill or brush off. It works. Also useful for oil spillages on driveways. Get the cheapest cola from the supermarket.
Before you apply powerful remedies... Are the tiles ceramic i.e. not lino? Have you tried washing/scrubbing with warm/hot water and soap or detergent?
What age is the house? Is it a Listed Building?