The spontaneous growth of cloud condensation nuclei (CCN) into cloud droplets under supersaturated water vapour conditions is described by classic Kohler theory(1,2). This spontaneous activation of CCN depends on the interplay between the Raoult effect, whereby activation potential increases with decreasing water activity or increasing solute concentration, and the Kelvin effect, whereby activation potential decreases with decreasing droplet size or increases with decreasing surface tension, which is sensitive to surfactants(1). Surface tension lowering caused by organic surfactants, which diminishes the Kelvin effect, is expected to be negated by a concomitant reduction in the Raoult effect, driven by the displacement of surfactant molecules from the droplet bulk to the droplet-vapour interface(3,4). Here we present observational and theoretical evidence illustrating that, in ambient air, surface tension lowering can prevail over the reduction in the Raoult effect, leading to substantial increases in cloud droplet concentrations. We suggest that consideration of liquid-liquid phase separation, leading to complete or partial engulfing of a hygroscopic particle core by a hydrophobic organic-rich phase, can explain the lack of concomitant reduction of the Raoult effect, while maintaining substantial lowering of surface tension, even for partial surface coverage. Apart from the importance of particle size and composition in droplet activation, we show by observation and modelling that incorporation of phase-separation effects into activation thermodynamics can lead to a CCN number concentration that is up to ten times what is predicted by climate models, changing the properties of clouds. An adequate representation of the CCN activation process is essential to the prediction of clouds in climate models, and given the effect of clouds on the Earth's energy balance, improved prediction of aerosol-cloud-climate interactions is likely to result in improved assessments of future climate change.