Cut half of the cucumber into slices, set aside, peel and chop the remainder of the cucumber. Place the pieces of cucumber in a blender. Tear off the basil leaves and add. Halve the lime, squeeze out the juice, add along with the water and acacia honey, puree in the blender.
Pass the cucumber juice through a sieve.
Place the ice cubes in the glasses. Combine the cucumber juice with the mineral water, pour over the ice cubes, add a couple of cucumber slices, serve the remaining cucumber slices with the drink.