X-ray sources with high photon fluxes and small source sizes have been widely pursued in the last decades. With synchrotron and XFEL facilities being complex, scarce and not easily accessible, laser-driven x-ray sources have emerged as a promising option because of their compactness, high photon yield and micrometric source size. In this work, we present the optimisation of an x-ray source driven by means of 0.8 mJ, 35 fs laser pulses focused on a solid Cu target in air. A detailed characterisation of the main x-ray beam parameters is included. A Cu Kα flux of 2.3·109 photons/s has been measured in 2π sr. Despite the simplicity of our setup, this flux is competitive with respect to that achieved with vacuum-based sources. A clear non-isotropic distribution of the x-ray continuum has been recorded, differing from the isotropic emission reported in dedicated studies. The beam is emitted within a cone with a semiangle of ≈14°, directed primarily along the target normal. Given the achieved flux, this source stands as a competitive alternative to more complex laser-driven x-ray sources operating in vacuum or in a He environment.