Strategies for achieving carbon emissions goals presuppose changes in individual behaviour which can be indirectly nudged by interventions or tailored information but ultimately depend upon individual attitudes. Specifically, the perception that climate change is low risk has been identified as a barrier to participation in climate change adaptation and mitigation efforts. Therefore, understanding public attitudes towards climate change risk is an important element of reducing emissions. We applied k-means cluster analysis to explore attitudes to climate change risk in the UK population using data from the UK Household Longitudinal Study, a national survey running from 2009 to present. We identified three distinct attitude clusters: “Sceptical”, “Concerned”, and “Paradoxical” in both waves 4 (from 2012 to 2014) and 10 (from 2018 to 2020) of this survey. The Sceptical cluster tended to deny the seriousness of climate change and the urgency or even the necessity of dealing with it. The Concerned cluster displayed anxiety about climate change risks and supported action to reduce them. The Paradoxical cluster acknowledged the reality of climate change impacts but did not support actions to mitigate them. We further observed statistical associations between cluster membership and the social characteristics of the participants, including sex, age, income, education, and political affiliation. We also found a temporal stability of cluster structure between the two waves. However, the transition matrices indicated a general transition away from the Sceptical and Paradoxical clusters, and toward the Concerned cluster between wave 4 to wave 10. The findings suggest that more tailored public information campaigns regarding climate change risk may be necessary.