Preheat the oven to 170 degrees C. Line a 2 lb loaf tin with baking parchment or a loaf tin liner.
Tip the sugar and butter into a large bowl. Cream together until light and fluffy.
Crack the eggs into the bowl one at a time and beat until combined.
Fold in the flour carefully, making sure that all of the flour is incorporated into the batter.
Add the treacle, stem ginger and ground ginger. Mix.
Tip the batter into the prepared cake tin. Bake for 1 hour until risen and cooked through.
Remove from the oven and leave to cool completely.
Mix together the lime juice, most of the lime zest and the icing sugar in a bowl. Drizzle the icing over the cake, then sprinkle over the rest of the lime zest.