Current translation for Hadlow Down
  had derived from hæsel/hæƿ  – hazel trees / heath or wasteland where heather grows
  low derived from hleow  – A shelter, protection, covering, refuge
  down derived from dun/dune  – a hill, mountain - however a significant number of downs appear to be near old Celtic hillforts
“Hazel trees hill, mountain shelter, protection, covering, refuge”
Place name translation provided by saxonhistory.co.uk