Preheat oven to 190°C/Gas 5 and line muffin tin with cases. Cream the butter and brown sugar until fluffy. Combine with the apple, carrot, milk and eggs. Combine the flour, bran, baking powder, baking soda and salt. Blend into original mixture and add walnuts.
Spoon mixture into muffin cases and bake. Turn out onto a wire rack.