Preheat oven to 180°C/Fan 160°C/Gas 4. Grease a 900g loaf tin with a little butter then line the base and two long sides with a piece of non-stick baking paper.
Cream the butter and sugar together in a large bowl with an electric mixer until light and fluffy. Gradually add the eggs, beating well after each addition and spooning in a little of the flour to stop the mixture from separating.
Fold in the remaining flour, baking powder and lime zest, then gradually add the gin. Spoon into the prepared tin, level the surface and bake for 55–60 minutes or until a skewer inserted into the centre comes out clean.
Meanwhile, make the sugar syrup: gently heat the caster sugar and tonic water in a small pan, stirring often, until the sugar dissolves.
Turn up the heat and boil for 1 minute. Spoon 2 tablespoons of the syrup into a small bowl and mix in 2 tablespoons of the gin (this mixture will be used to soak the loaf later).
Add the thinly sliced lime to the remaining tonic syrup in the saucepan. Bring to the boil and cook for 5–7 minutes until the lime slices are soft and the syrup thickened.
Spoon the lime slices over a baking sheet lined with non-stick baking paper, draining off some of the syrup and leave to cool.
As soon as the loaf comes out of the oven, poke holes into the top with a skewer and drizzle over the reserved gin syrup from the bowl. Cool the loaf in the tin on a wire rack.
Make the icing by mixing together the sifted icing sugar with the remaining 1½ tablespoons gin until smooth.
Remove the loaf from tin, transfer to a board and peel off the paper. Spoon over the icing and decorate with the lime slices. Leave the cake to set before slicing.