Observed correlations between short-term decreases in cosmic ray ionisation and cloud and aerosol properties have been attributed to short-term decreases in the ion-induced nucleation rate. We use a global aerosol microphysics model to determine whether a 10 day reduction of 15% in the nucleation rate could generate a statistically significant response in aerosol concentrations and optical properties. As an upper limit to the possible effect of changes in ion-induced nucleation rate, we perturb the total nucleation rate, which has been shown to generate particle concentrations and nucleation events in reasonable agreement with global observations. When measured against a known aerosol control state, the model predicts a 0.15% decrease in global mean cloud condensation nucleus concentration at the surface. However, taking into account the variability in aerosol, no statistically significant response can be detected in concentrations of particles with diameters larger than 10 nm, in cloud condensation nuclei with diameters larger than 70 nm, or in the Ångström exponent. The results suggest that the observed correlation between short-term decreases in cosmic ray ionisation and cloud and aerosol properties cannot be explained by associated changes in the large-scale nucleation rate.