Neutron stars are strongly magnetized rotating compact objects. Therefore, they also produce huge electric fields accelerating particles to ultrarelativistic energies. The simplest magnetic topology is a dipole traditionally located at the stellar centre. In this paper, we re-investigate the consequences of an off-centred rotating magnetic dipole, showing accurate magnetic field line geometries, the associated spin-down luminosity as well as the corresponding electromagnetic kick and torque imprinted to the neutron star. Results are obtained by time-dependent numerical simulations of Maxwell equations in vacuum using pseudo-spectral methods. We compare our results to known analytical expressions available to lowest order in the parameter ϵ = d/R, where d is the displacement of the dipole from the stellar centre and R the neutron star radius. We found good agreement between our numerical computations and our analytical approximations even for well off-centred dipoles having large displacements with a sizeable fraction of the radius, i.e. ϵ ≲ 1. An explanation for binary neutron star eccentricity distribution functions is given with an emphasize on highly eccentric systems as an alternative scenario to traditional binary formation.