Cream the oil or butter with the honey in a mixing bowl. Gradually beat in the egg. Mix in the carrots or apples, bananas and flour (All-purpose flour may be used with 1/2 tsp baking powder); add the raisins, cherries, cranberries, or prunes and zest. Add a little extra flour, if necessary, until spoon stands upright in the mixture.
Turn the mixture into a greased 7in shallow, square cake pan and level the surface. Bake until golden brown, about 40-45 minutes.
Cool slightly, then lightly score into finger-shaped slices using a sharp knife. Cool completely in the pan, then cut into fingers and serve.