What is the minimal set of ingredients that English rice pudding can be made with?
The absolute minimalist version needs 2 ingredients:


1 part short-grain rice, cooked in
4 parts milk


If cooked long enough and especially when stirred diligently, the rice will release enough starch to create a creamy, mushy texture, like risotto. But for rice pudding, the rice is usually cooked softer than risotto, which should have a bit of a “bite”.

You can stop at this point and will have a perfectly fine dish, but probably a bit on the bland side, with just a hint of sweetness from the starch and milk. But it can be a neutral base for fresh fruit, applesauce, ...

I personally would always add a pinch of salt and, if going for an especially rich taste, a splash of cream when fully cooked. 

All spices are optional, they change the flavor profile and that’s where the cook’s creativity can shine. Roughly the same is true for sugar or other sweeteners. (I like to add sugar after cooking, sometimes even as topping for each serving, because I feel that cooking without sugar reduces the risk of sticking/burning and because it seems that I need to add less for the same perceived sweetness.)