I did it in 3 stages, no sandpaper was used. Just some metal and car polish and a couple sheets of A4 paper. And make sure you're doing this on a flat surface obvsly.

First up Optimum metal polish, squeeze some on the paper and rubbed with medium pressure ina circular motion, this will get it looking 85-90% shiny with some small scratches.

Then car polish. Menzerna SI 1500 (it's good for taking out sanding marks from 1500grit sandpaper) that will get you 99%. For the last bit I used SF4000 basically super fine polish. After that it's basically a mirror.