With the aim of understanding discrepancies between experimental observations and numerical simulations for a cylinder rolling down an inclined plane, this study investigates the effect that offsetting the centre-of-mass from the cylinder centroid has on body forces, velocity and wake structures. The numerical cases considered focus on the same parameters as the referenced experiment: cylinder-to-fluid density ratio and wall inclination angle, for Reynolds numbers in a range around the critical value for the transition from stationary flow to periodic vortex shedding. The centre-of-mass is placed at a distance of up to 2 % of the diameter from the geometrical centre of the cylinder. It is found that the main features of the predicted wake flow are in good agreement with those observed experimentally. They include the inception of small-scale shear-layer vortices in the near wake, locked to the cylinder rotational frequency, as well as large-scale vortices further downstream. This is further confirmed through force and velocity histories, where two oscillations are found to operate at significantly different frequencies. While the amplitudes of the lift, drag and cylinder velocity oscillations see an increase with offset distance, the Strouhal numbers of the small- and large-scale structures remain unaffected and agree well with those measured in experiments at similar Reynolds numbers.