As Pea pod says, Steredent tablets, although i'd say boiling water instead of warm.
I used to use a tea can for work, (train driver), and it really got stained, Steredent tablets, got it clean as a whistle.
I use Sterilizing fluid (like Milton) for cleaning stains off coffee cups etc. Works really well. You don't have to buy Milton there are lots of cheap alternatives.