@runner101 - Figgy pudding is a kind of steamed fruit cake so I would guess the song was adapted to fit because 'hasty pudding' was more meaningful, rather than the two dishes being anything alike.
I can't say that either sound very appetising to me. I do like traditional foods, but being English my favourite is bread and butter pudding. It may only be bread, butter, sugar, dried fruit, eggs and milk all baked together, but it is unbeatable.
It sounds like hasty pudding is bland unless you add something sweet to it. Isn't it easier to just make a delicious dish from the get go?