I might be late to the party but I have only just discovered this to deal with heavy brown tea staining (which also makes the mug surface rough).
Half a scoop of Vanish Oxi-Action in the mug, add boiling water, leave for 10-15 minutes, and the brown stain just lifts off like magic in a sort of 'skin'. Quite odd, I didn't expect it. You then rinse the mug and lightly scrub a few small bits, but the end result is like new and the glaze perfectly smooth again.
Again, sorry if you all know about this already!