Cook the beetroot, in its skin, in plain water until very soft. Drain and leave to cool. Peel the beetroot while still warm. Ensure that you wear gloves for this to avoid the purple flesh staining your hands a deep red.
Chill the beetroot well.
In a blender, combine the ice, honey, and lemon juice and blend well to a smooth pulp.
Turn on the blender to high speed and incorporate the orange juice. Adjust the lemon and honey to taste and serve well chilled.