  We analyse in a systematic way the (non-)compact n-dimensional Einstein Weyl
spaces equipped with a cohomogeneity-one metric. With no compactness
hypothesis, we prove that, as soon as the (n-1)-dimensional space is an
homogeneous reductive Riemannian space with an unimodular group of left-acting
isometries G
  1)a non-exact Einstein-Weyl stucture may exist only if the (n-1)-dimensional
homogeneous space G/H contains a non trivial subgroup H' that commutes with the
isotropy subgroup H,
  2) the extra isometry due to this Killing vector corresponds to the
right-action of one of the generators of the algebra of the subgroup H'.
  We also prove that the subclass with a one-dimensional subgroup H'
corresponds to n-dimensional Riemannian locally conformally K\"ahler metrics,
the (n-2)-dimensional space G/(HxH') being an arbitrary compact symmetric
K\"ahler coset space.
