hi the best way is to use a mechanichal scrubber but as its a galley kitchenthis will be to big so bear with me hear go`s.
firstly you need to get hold of some ltp grimex mix in warm water as per instructions and soak a workable area of floor ,do not cover more floor than you can reach or you will get in a mess about a mtr wide at a time is enough then leave 10to 15 mins.(do not allow to dry out)
after the floor has soaked scrub vigoursly with a stiff scrubbing brush preferably nylon make sur grout joints are scrubbed realy well.
sponge floor over rinsing with plenty of clean water.
repeat this for the rest of the floor not to much at a time, when floor is done alow 24hrs to dry (do not walk on floor with dirty footwear of spill any thing on it at this stage or allow animals on it.
after 24 hrs seal floor with impregnating sealer such as ltp mattstone or colour intensifier or a surface sealer such as ltp iron wax.
sorry a bit long winded but its worth it i have been stripping and resealing stone and terracotta for 8yrs and this will work.