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Thanks for all the advice guys, went with the ceramic cleaner as that's what I had, took seconds to get to this! So much easier than scrubbing with Hoppes & CLP!
If you look at the contents, Cerama-Bryte is very similar to good, old-fashioned Bon-Ami, ie basically powdered feldspar and therefore an exceedingly mild abrasive. If you can find Bon Ami it's way cheaper than Cerama Bryte. (They make two formulas, the "original" and the new, improved one. Ironically the new version, although it has more stuff in it, is cheaper than the original.)
Personally, I use Ed's Red and a nylon brush (a toothbrush might work, too.)