[Rosie] Yes, they did have rum until July 1970 (one eighth of a pint per day), which I think was issued as two-water grog (watered-down 2 parts water to 1 part rum). Pusser's Rum has been made since about 1980 to the old Admiralty recipe and a donation goes to the Royal Navy Sailor's Fund from every bottle sold. I have some of the blue label, bottled at 54%abv, and it's quite a fierce nip if you don't water it down at all. However, when the officers gathered for a social in their mess, the poor midshipmen (officer cadets, essentially) would have to join in, and behave like an officer, while on a phenomenally meagre wage, hence the most popular cheap, "sophisticated" drink for them (i.e. not neat spirits or beer) was pink gin.
[Phil] You may have just enlightened me. I've heard my father (who was in the Navy), talk about 'Pussers Kai'. I thought, in the context, it was cocoa with a slug of rum. This now looks likely and a quick google supports that. However this was a long time before 1980.
[INJ] Ah, Kye (the spelling I've grown up with)! I've found some web sites that describe it as thick cocoa made with condensed milk, but according to my RN dad, it was cocoa made with water and no milk at all. As he's a hardy soul, that's still how my dad makes cocoa. It takes some getting used to, but it's OK.