Social mobility is high on the policy agenda and is an important component of reducing inequalities. Estimating the relationship across generations of multiple dimensions of mobility such as health and wages can be used to understand the current state of mobility. However, there has been little research on how policy impacts on the relationship of multiple outcomes across generations and how that may be contributing to health inequalities and long-term mobility. In this paper, we use the UK as a case study to evaluate the impact of three distinct policy periods: 1991–1998 (Increasing neo-liberalism); 1998–2009 (English Health Inequalities Strategy); 2010–2017 (Austerity) on the relationship across generations in health (self-assessed health (SAH) and mental health measured by General Health Questionnaire 12 (GHQ-12)) and hourly wages. We employ fixed effects models on data from the British Household Panel Survey (1991–2008) and its successor the Understanding Society Survey (2009–2017). To investigate the role of policy on inequalities, sub-group analysis is performed by parental socioeconomic status measured by parental educational attainment, parental occupation, and if a single parent household. Results show that for the population on average, a changing policy focus has no impact on the strength of the relationship across generations in both health and wages. However, when looking at sub-groups the strength of the relationship in SAH and wages is increasing for parents with basic and higher qualifications and their young adult children. Whereas the influence of parents on their young adult children’s SAH, mental health, and wages has remained fairly constant over the period 1991–2017 for parents with manual occupations and professional occupations. There has been a slight weakening in the influence of parents on their young adult children’s SAH and wages for single parent families from 2010.