Is it true that new mobile phone batteries should be charged for 16 or more hours, then run down in the phone, and repeated twice more? Or just charged until ready. The same query would apply to camera batteries (li-on).

I used to work for a large American Cell phone company,
According to them the initial charge should be at least 3 hours. You shouldn't do partial charge on the first charge.
Any time after that it just depends on how long you have to wait. They don't recommend leaving them on the charger ALL the time or after they have finished charging.
Your manuel should tell how long for your specific model.

Thanks for that. There was no mention of how long to charge in the manual- I did look!

No worries, I know each phone is different, but I have never heard of a phone taking 16 hours!
Usually it is 3-4 hours depending on the continuois talk time on your phone.