Hi Antony
It sounds like non-codeine tablets would be OK but if I were you I would contact the embassy with the name of any products you plan to take, as the FCO site suggests.
I found these contact details on the embassy website - emailing them is probably simplest.
Telephone enquiries 020 7465 6543 / 6544
Email info@ld.mofa.go.jp
Kind regards,
Olly, your editor