Cut the cucumber lengthways and use a spoon to scrape out the stones. Remove long thin strips from the cucumber with a potato peeler.
Fill eight tall glasses with ice cubes, divide the elderflower syrup, Prosecco and tonic water between them, as well as the cucumber strips and the mint leaves. Squeeze a lime wedge over each glass and then drop it into the glass. Swirl the drinks gently to mix them.