Best way to clean textured floor tiles

[gasman]

I get the keys to my new home on Thursday.

It has pale textured floor tiles in the kitchen and bathroom (stone effect). These have been neglected and have masses of engrained dirt.

I've never had a tiled floor before - I'm more of a vinyl person - and haven't got a clue about cleaning such things.... I need to do so as a new kitchen isn realistically a year away.

So steam mop but the spaces are tiny - kitchen is about 1.5mx3m overall and a lot of that is taken up by cabinets), scrubbing brush and floor or magic product that you slosh on which lifts the dirt?