Line a 23cm/9in square cake tin at least 4cm/1½in deep with baking parchment.
Preheat the oven to 160C/325F/Gas 3.
Place the butter, sugar, golden syrup and black treacle into a pan and heat gently until the mixture has melted evenly. Set aside to cool slightly.
Sift the flours, ground ginger and stem ginger into a large mixing bowl and mix gently. Pour the cooled butter mixture into the flour. Add the eggs and milk and beat with a wooden spoon until well combined.
Pour the cake batter into the tin and level the surface with a palette knife or the back of a spoon. Bake for 50 minutes, or until the cake has risen and is golden-brown and a skewer inserted into the middle comes out clean. Set aside to cool slightly in the tin, then transfer the cake to a wire rack and set aside to cool completely.
Meanwhile, for the orange icing, sift the icing sugar into a bowl. Add about two tablespoons of the orange juice and mix to a smooth paste. Add more orange juice, as necessary, until you get a smooth icing of the consistency you desire.
Pour the icing over the cooled cake and spread lightly, allowing it to ooze over the edges. Sprinkle over chopped orange zest and set the cake aside until the icing has set.
To make it easier to measure out syrup and black treacle, warm a metal spoon in boiling water.