Mop the floor with warm water and a cap full of distilled vinegar. Allow to dry.
Mix bicarbonate of soda (baking powder will not do) with water. Begin with around the same volume of both in a tub. Brush this paste onto the floor, one tile at a time, using an old paint brush. Each brush load should be a mixture of water and bicarb. Add a splash more water into the container each time the paste becomes too thick. Allow to dry.
Spray the covered tiles with distilled vinegar. Ensure the entire surface is covered with vinegar as it’s this that activates the bicarb and lifts the dirt. Allow to dry.
Mop the floor with clean warm water.