Haha, I didn't realize that pudding meant cake in England. I only learned that in Harry Potter and the chamber of secrets, when dobby makes the cake splatter on the Mason's at the dursley house.
In England pudding isn't cake, it's pudding. Like summer pudding, spotted dick, Christmas Pudding, steak and kidney pudding etc. Or, it's an alternative word for dessert. Cake is not pudding, but you can have cake FOR pudding.