For the cake: Heat the oven to 160 degrees celsius/gas 4 (320 degrees F). Grease a 22-by-22-centimeter (8-by-8-inch) baking pan with butter and dust with flour. Line with parchment paper.
Using an electric mixer, cream the sugar and butter in a large bowl until the sugar has dissolved and the mixture is pale. Add the eggs one at a time, beating well after each addition. Add the glucose and mix well. Sift the flour and baking powder together, and then fold into the batter to incorporate. Add the double cream and coconut; mix well. Stir in the lime zest and lemon zest.
Pour half of the batter into the prepared pan and smooth the top. Dot with the jam in evenly-spaced spoonfuls. Cover with the remaining batter and smooth the top. Bake until the cake is golden and well-risen, 50 to 60 minutes. Let cool on a wire rack.
For the icing: Mix together the confectioners' sugar and lemon juice to form a smooth paste.
Remove the cake from the pan and place on a serving dish. Brush the top with the icing, sprinkle with lemon zest and scatter with rose petals.