With thanks to all those who advised me about cleaning my badly tea-stained teaspoons. I wanted to let all know what worked very well for me in the end, in case it also helps anyone else.
I happened to have on hand a cheap bleach powder, a generic brand of powder bleach whose ingredients are said on the packet to be "Soda Ash" and "Peroxygen" - "contains NO phosphorous".
To be sure, I left three teaspoons standing for three days in a strong solution of this bleach and hot water (did not change the water). It might not have needed three days, but I was in no hurry.
They came up perfectly! *Very* shiny. All they needed was to be rinsed off.
Thank you all,
avril