Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
MEDHURST
As described in historical dictionaries
Patronymica Britannica (1860)
MEDHURST. Probably either Midhurst or Madehurst, both parishes in Sussex. De Medhurst. H.R. co. Kent.