New particle formation has been estimated to produce around half of cloud-forming particles in the present-day atmosphere, via gas-to-particle conversion. Here we assess the importance of new particle formation (NPF) for both the present-day and the pre-industrial atmospheres. We use a global aerosol model with parametrisations of NPF from previously published CLOUD chamber experiments involving sulphuric acid, ammonia, organic molecules and ions. We find that NPF produces around 67% of cloud condensation nuclei at 0.2% supersaturation (CCN0.2%) at the level of low clouds in the pre-industrial atmosphere (estimated uncertainty range 45-84%) and 54% in the present day (estimated uncertainty range 38-66%). Concerning causes, we find that the importance of biogenic volatile organic compounds (BVOCs) in NPF and CCN formation is greater than previously thought. Removing BVOCs and hence all secondary organic aerosol from our model reduces low-cloud-level CCN concentrations at 0.2% supersaturation by 26% in the present-day atmosphere and 41% in the pre-industrial. Around three-quarters of this reduction is due to the tiny fraction of the oxidation products of BVOCs that have sufficiently low volatility to be involved in NPF and early growth. Furthermore, we estimate that 40% of pre-industrial CCN0.2% are formed via ion-induced NPF, compared with 27% in the present-day, although we caution that the ion-induced fraction of NPF involving BVOCs is poorly measured at present. Our model suggests that the effect of changes in cosmic ray intensity on CCN is small and unlikely to be comparable to the effect of large variations in natural primary aerosol emissions