Just had a little google read up on this. Before reaching for the sander you could try white spirit if the paint splatters are oil based and scrape with plastic or wood scraper so as not to scratch the slate. Nail polish remover (acetone) might also work. If there was previously a sealant any paint thinner will remove this as well so it would need re-sealing after. If it’s acrylic or water based paint isopropyl alcohol or even baby wipes might do the trick. Natural slate is a porous material meaning if any stains have absorbed deeply then they’ll be hard to remove. I did read about another chemical process but it’s very complicated and toxic and should really only be carried out by a professional. As Jonathan said it’s probably cheaper to buy a new hearth but if you find a method let us know.

How lovely! In the olden days (even before my time) cast iron grates and fireplaces were blackened with a special paste polish and then buffed. I’m not sure about the rust though. Something like this, but there are other brands.

Love how sturdy it this table looks. Personally If I were to buy it I'd want it unrestored as I like doing it myself. As you are planning to sell it, its more than likely the buyer has a look in mind and most probably would restore it to suit their style.

Thanks Sonia, there are quite a few scuffs like the one I’ve put up of the close up so I think I’ll need to do something. Will start with a clean and see how it looks. Unfortunately in some places the top layer of brass coloured coating has come off where it’s scratched. Wondering if I could take it somewhere for a professional to do it? If there is such a place!