Current translation for Hailsham
  hail derived from hæg/haga - an enclosure / a haw, berry of the hawthorn
  sham derived from hamm - Denotes a piece of land surrounded with paling, wicker-work, etc., and so defended against water, which would otherwise wash it away, so a valley settlement or settlement with a jetty.
Found in Domesday 1086AD
Name found:Hamelesham(Sussex)
Place name translation provided by