Grease a 20 cm (8 inch) round springform cake tin and line the base with nonstick baking paper.
Beat the butter, sugar and grated lime rind together in a large bowl with a hand-held electric whisk until pale and fluffy. Beat in the eggs a little at a time, adding 1 tablespoon of the flour if the mixture starts to curdle, then fold in the flour and coconut with a large metal spoon.
Spoon into the prepared tin and bake in the centre of a preheated oven, 180°C (350 °F), Gas Mark 4, for 35–40 minutes until risen and golden and shrinking away from the tin.
Leave to cool in the tin. While still warm, mix the sugar for the topping with the lime juice and spoon over the cake. Sprinkle over the coconut and lime rind strands. Leave to cool completely.