Occasional maintenance is needed on your fireplace, including the grate, hearth and surround, whether they are cast iron, slate or marble.
Remove dirt with methylated spirit; apply it on a cloth, changing the cloth until no more dirt comes off. Make sure you do not flood old tiles with the spirit as it will penetrate any cracks in the glaze.
Buff the grate to a dull sheen using black lead or graphite grate polish. This is applied very sparingly and vigorously with a brush, and polished gently with a soft cloth two hours later. If the metal of the grate is very smooth, you may find the polish does not stick. Try dabbing it on and leaving it for two hours. If it still comes off again, use some very fine sandpaper to roughen the metal before trying again.
A more modern alternative is a thin coat of matt black stove paint, a coating of wax, and then polish.
To clean smooth slate, dip a cloth in water with washing-up liquid and wring it out. Scrub the slate thoroughly. Then use a clean, damp cloth to wipe the slate. Use a dry cloth to buff it up.
If this is not effective, you may need to clean it more thoroughly and then use slate oil. Swab the slate with white spirit and then sponge it off. Repeat a couple of times and allow to dry. Then use the slate oil.
To clean rough slate, use a scrubbing brush with washing-up liquid, and rinse thoroughly. Do not use oil.
Remember that marble is porous and will dissolve in acids; for example, wipe up red wine immediately.
To clean marble, dissolve soap flakes in water. Dip a cloth in the soapy water and wring it out. Scrub the marble thoroughly. Then use a clean, damp cloth to wipe it and use a dry cloth to buff it up.
You can use an oil-based finish for polishing the marble.
To clean up soot, use a vacuum cleaner to remove any loose soot. It may be best to hire an industrial machine. Spray the rest of the soot with a weak solution of water and caustic soda and scrub. Then spray the area with a weak solution of water and clear vinegar to neutralise any remaining caustic soda. Repeat the process as necessary, mopping up regularly.