For elderflower ice-cream, combine cream and lime rind in a saucepan and bring just to the boil over medium heat. Remove from heat and stand for 10 minutes to infuse, then return to heat and bring just to the boil again. Meanwhile, whisk together egg yolks and sugar until thick and pale, then whisk in elderflower cordial. Pour over cream mixture, whisking to combine, return to pan and cook, stirring continuously, over medium heat until mixture thickly coats the back of a spoon (4-5 minutes). Strain through a sieve into a bowl placed over ice, whisk in lime juice, then cool completely in refrigerator. Freeze in an ice-cream machine according to the manufacturer’s instructions. Makes about 2 cups.
Combine sugar and 1 cup water in a small saucepan over medium-high heat and stir until sugar dissolves. Add lime slices, and bring to the boil, then reduce heat to low and simmer until lime is tender and translucent (about 10 minutes). Using a slotted spoon, carefully remove candied lime slices and transfer to a plate. Squeeze excess water from gelatine, add to syrup, remove from heat and stir until gelatine dissolves. Add tonic water and gin and stir well to combine.
Divide mixture among four ¾ cup-capacity serving glasses and refrigerate until beginning to thicken slightly (3½-4 hours), then drop a candied lime slice in each glass and refrigerate until set (about another hour). Serve jellies with elderflower ice-cream and remaining candied lime slices to the side.