Sift the flour, baking powder, cinnamon and nutmeg on to a plate, add the rolled oats and chopped walnuts and set aside.
Cream the butter in a basin, then beat with the sugar until light. Lightly mix the eggs with the vanilla essence, lemon rind and juice and beat into the creamed mixture a little at a time. Fold in the flour mixture, along with the extra milk if needed, to make a soft consistency. Spoon into a medium-sized greased and lined shallow baking or roasting tin and spread the top smoothly. Bake in the centre of a moderate oven (180°C., 350°F., Gas Mark 4) for 30–35 minutes until golden brown. Remove from the oven and set aside while preparing the glaze.
Sift the icing sugar and mix to a smooth glaze with the lemon juice. Pour over the top of the warm cake and spread smoothly. When the cake is cold, loosen the sides and lift from the tin. Cut into squares.