Here's a recipe for a milk-free birthday cake I found accompanying a news article at the Scotsman:

Ingredients:

1½ cups egg whites
½ teaspoon cream of tartar
¼ teaspoon Baking powder
1 teaspoon vanilla extract
½ teaspoon ground cinnamon
¼ cup rolled oats
3 ripe bananas, mashed
1 cup cake flour
2 cups confectioners' sugar
¼ teaspoon salt

Method:

Preheat oven to 165C.

Beat egg whites until stiff but not dry.

Combine cream of tartar, baking powder, vanilla, cinnamon, oats, and mashed bananas. In a separate bowl combine the flour, confectioner's sugar, and salt.

Fold the banana mixture into the egg whites. Then fold the flour mixture into the egg white/banana mixture.

Pour batter into one 9 or 10 inch round cake pan, coated with a non-stick cooking spray.

Bake for 1 hour, until cake is firm and lightly golden.

Cool for five minutes then slip out of pan on to a serving dish. Garnish with a light dusting of confectioner's sugar.

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The article itself is a little garbled; it was about a mom's plight to find a dairy-free birthday cake for her son. I didn't quite get it whether the child had milk allergies or lactose intolerance. Anyway, looking at the ingredients, this cake recipe should be good for either condition. How does it taste like? Let me know if you try it out!