Cleaning a cast iron bath

I installed a cast iron bath I got on Done Deal during a build without paying too much attention to the dirt of it (I reckoned a good scrub would bring it back pristine). Turns out it's staining that gives the dirty appearance, not surface grime.

I know you can baths recovered but am wondering whether there are any super-dooper chemicals which would clean the bath - as a first port of call. I've tried elbow grease and neat bleach without any effect.

Thanks..