There have been 65 post in response to this. I haven't time to read them, Busy Busy - but might I suggest - if it hasn't already been done - that you consider an alternative approach to this problem.
Dear Heart and I are genteel people who care about the planet, each other and our personal inner workings.
The type of product you use for cleansing your soiled crockery should only be Ecover washing up liquid - environmentally friendly and thus satisfying all criteria in terms of the planet.
E.H. Booth and Co. is a local family run supermarket and they stock a rather fine Min China Tea. We drink this as it is light and refreshing and so does not contain the tannin levels in what I presume is one of the rather more common brands which you use.
Consider the effect on your personal workings in comparison to the crockery you are endeavouring to rid of unsightly brown stains. I would also ask you to consider the fate - in order that you might avoid a similar demise - of the great Shawnee American Indian Chief - Two Dogs - who died in his TeePee.
Whatever you do - clean cups by the 10th please
affectionately as ever....
From off the tossing of these fiery waves;
There rest, if any rest can harbour there;
And, re-assembling our afflicted powers,
Consult how we may henceforth most offend
Leave the stains alone. Use paper cups if it bothers you. When you bring out your best tea stained china for guests any that object are to bloody fussy to be on a boat.