Although White 1932, and others, give this as English, it seems to originate from Berkeley in the USA, where it is known since 1865.
Original Receipt from 'What to do with the cold mutton - a book of rechauffes together with many other approved receipts for the kitchen of a gentleman of moderate income', by 'PKS', New York, 1865No 238 THE BERKELEY PUDDING
Take one pound of suet chopped very fine, four ounces of flour, half an ounce of fine bread crumbs, three whole eggs, half a small tea spoonful of pounded mace, the same of cinnamon, a little grated nutmeg, a little grated lemon peel, and half a pint of milk; mix all together, put into a plain mould and boil nine hours. For the sauce make a custard with the yolks of two eggs, white sugar to taste and a wine glassful of rum.