- Ultra-intense MeV photon and neutron beams are indispensable tools in many research fields such as nuclear, atomic and material science as well as in medical and biophysical applications. For applications in laboratory nuclear astrophysics, neutron fluxes in excess of 1021 n/(cm2 s) are required. Such ultra-high fluxes are unattainable with existing conventional reactor- and accelerator-based facilities. Currently discussed concepts for generating high-flux neutron beams are based on ultra-high power multi-petawatt lasers operating around 1023 W/cm2 intensities. Here, we present an efficient concept for generating γ and neutron beams based on enhanced production of direct laser-accelerated electrons in relativistic laser interactions with a long-scale near critical density plasma at 1019 W/cm2 intensity. Experimental insights in the laser-driven generation of ultra-intense, well-directed multi-MeV beams of photons more than 1012 ph/sr and an ultra-high intense neutron source with greater than 6 × 1010 neutrons per shot are presented. More than 1.4% laser-to-gamma conversion efficiency above 10 MeV and 0.05% laser-to-neutron conversion efficiency were recorded, already at moderate relativistic laser intensities and ps pulse duration. This approach promises a strong boost of the diagnostic potential of existing kJ PW laser systems used for Inertial Confinement Fusion (ICF) research.