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Pop in a proper tiling shop (not Homebase etc) and have a chat. There are loads of really good cleaning products, some more corrosive/aggressive than others. You want something that won't damage the stone, whilst lifting the greasy gunk and left over soap etc, that will have built up. Once it's clean (and I mean CLEAN!) I can recommend a product called 'antidrop', which depending on how you want it to look, can either be Matt, satin or gloss. I like satin finish on those...I've fitted hundreds of metres of natural stone, as most tilers steer clear of it, for the reasons you've discovered!
I'm not having a pop at your cleanliness by the way, it's just that it needs to be very clean before sealing, as the finish is better!
Thanks that seems fairly comprehensive. Do you have a method for cleaning? It’s our utility room so washing machine and drier aside, we can be quite disruptive.