We report a systematic study of low-field galvanomagnetic properties of aluminium-based dilute alloys with 3d and 4sp impurities. The low-field magnetoresistivity tensor is determined by exactly solving the linearized Boltzmann equation for the anisotropic vector mean free path, without using any adjustable parameter. Our method of calculation is based on the on-Fermi-sphere approximation which allows us to combine the full anisotropy of the host Fermi surface, obtained by the four-orthogonal-plane-wave method, with the impurity scattering phase shifts, evaluated by self-consistent local-density-functional impurity-in-jellium calculations. Our results for the Hall coefficient and the magnetoresistance are in good agreement with the experimental data.