The relationship between living alone, loneliness and social isolation, and how they are associated with health remain contentious. We sought to explore typologies based on shared experiences of loneliness, social isolation and living alone using Latent Class Analysis and determine how these groups may differ in terms of their physical and mental health. We used Wave 7 of the English Longitudinal Study of Ageing (N = 7,032; mean age = 67.3) and responses to the University of California, Los Angeles (UCLA) loneliness scale, household composition, participation in social/societal activities plus frequency of contact with friends, family and relatives for the Latent Class Analysis. The optimal number of groups was identified using model-fit criteria. The socio-demographic characteristics of groups and health outcomes were explored using descriptive statistics and logistic regression. We identified a six-cluster typology: Group 1, no loneliness or isolation; Group 2, moderate loneliness; Group 3, living alone; Group 4, moderate isolation; Group 5, moderate loneliness, living alone; and Group 6, high loneliness, moderate isolation (with high likelihood of living alone). Groups experiencing loneliness and/or isolation were more likely to report poorer physical and mental health even after adjusting for socio-demographic confounders, this was particularly notable for Group 6. Our results indicate that different typologies of living alone, loneliness and isolation can be identified using data-driven techniques, and can be differentiated by the number and severity of issues they experience.