We are looking for guidance on how to clean/restore an original 1930s (UK) fireplace (photoed below). We are not sure what metal it is, but assume it is cast iron.
It's a cast iron fireplace, very common in Victorian times. First you'll need to find out if it's been painted or polished. Usually you can see just by looking at it, if you see brush marks or flaking areas it's been painted. A smooth finish which shows the metal finish probably means it's polished (my gut instinct, looking at the patina on yours is that it is polished).
Restoration depends on the level of unsightly areas. A painted fireplace can always be cleaned up and re-painted. Be careful if you suspect the original paint is old as it may contain lead (don't sandpaper it etc.). Use a heat resistant paint if you intend to use the fireplace (assuming the original paint is also heat resistant, which may be difficult to determine...).
A polished fireplace can be cleaned up with a stiff brush or wire wool and re-polished with a special black compound for cast iron grates/firebacks. We call it 'black lead' around here, but that is probably a throw back to earlier times as modern compounds do not contain lead. Modern names include 'grate polish' or 'graphite polish' or 'black polish' etc.