The structure of water and the nature of ionic hydration is explored in aqueous solutions of potassium fluoride, chloride, bromide and iodide over a range of concentrations up to 4.8 ion pairs per 100 water molecules, using the combined techniques of neutron diffraction with hydrogen isotope substitution. The diffraction data are interpreted using the method of empirical potential structure refinement, which attempts to build a three-dimensional model of the scattering system consistent with the diffraction data. The water structure is strongly perturbed in the first hydration shells of both anion and cation, but is found to be only mildly perturbed outside of this region, with the largest effects occurring with the smallest anion and highest concentrations. For the potassium ion there are strong orientational correlations in the first hydration shell, with the water molecules lying with their dipole moments pointing almost directly away from the cation on average, but with an angular spread of approximately +/-60 degrees which is mildly dependent on the anion type present. For all the anions the water molecules in the first shell are strongly oriented with one O-H vector pointing directly towards the anion on average, with an angular spread of approximately +/-10 degrees for F(-), increasing to approximately +/-22 degrees for I(-). For both anions and cations the second hydration shell is much more disordered than the first, but there is a weak pattern of orientational correlation which becomes more pronounced with the larger anions. There is some evidence that the fluoride ion structures water significantly in its first hydration shell, but not beyond. The findings throw further light on recent findings that the orientational relaxation time for water outside the first shell of dissolved ions is the same as in the bulk liquid.