Objective Scant evidence is available on the discordance between loneliness and social isolation among older adults. We aimed to investigate this discordance and any health implications that it may have. Method Using nationally representative datasets from ageing cohorts in Ireland (TILDA) and England (ELSA), we created a metric of discordance between loneliness and social isolation, to which we refer as Social Asymmetry. This metric was the categorised difference between standardised scores on a scale of loneliness and a scale of social isolation, giving categories of: Concordantly Lonely and Isolated, Discordant: Robust to Loneliness, or Discordant: Susceptible to Loneliness. We used regression and multilevel modelling to identify potential relationships between Social Asymmetry and cognitive outcomes. Results Social Asymmetry predicted cognitive outcomes cross‐sectionally and at a two‐year follow‐up, such that Discordant: Robust to Loneliness individuals were superior performers, but we failed to find evidence for Social Asymmetry as a predictor of cognitive trajectory over time. Conclusions We present a new metric and preliminary evidence of a relationship with clinical outcomes. Further research validating this metric in different populations, and evaluating its relationship with other outcomes, is warranted. Copyright © 2016 John Wiley & Sons, Ltd.