Health inequalities are often examined through single axes such as class or ethnicity, obscuring how these dimensions interlock. This study applies a longitudinal intersectional approach to examine physical and mental health trajectories across five generations in the UK. We analysed 14 waves of the UK Household Longitudinal Study (2009-2024) using longitudinal Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA). We modelled SF-12 physical and mental health trajectories for 398 intersectional strata defined by gender, ethnicity, occupational class, and generation. Physical health inequalities widened with age, consistent with cumulative disadvantage, while mental health inequalities were more evident among later-born cohorts. The 'Boomer' generation exhibited a relatively flat mental health trajectory across its observed age range. In contrast, 'Generation Z' had lower predicted mental health, particularly among White British women with no work history - a group with poorer predicted trajectories than their South Asian peers. Our study shows how health inequalities are structurally differentiated by cohort and intersectional position. Policy responses should support proportionate universalism, combining broad population-level support with intensified action for groups showing poorer health.