We report on the experimental observation of beam-like neutron emission with peak flux of the order of 10^9 n/sr, from light nuclei reactions in a pitcher-catcher scenario, by employing MeV ions driven by high power laser. The spatial profile of the neutron beam, fully captured for the first time by employing a CR39 nuclear track detector, shows a FWHM divergence angle of 70 degrees, with a peak flux nearly an order of magnitude higher than the isotropic component elsewhere. The observed beamed flux of neutrons is highly favourable for a wide range of applications, and indeed for further transport and moderation to thermal energies. A systematic study employing various combinations of pitcher-catcher materials indicates the dominant reactions being d(p, n+p)^1H and d(d,n)^3He. Albeit insufficient cross-section data are available for modelling, the observed anisotropy in the neutrons spatial and spectral profiles are most likely related to the directionality and high energy of the projectile ions.