This paper presents a novel approach to quantify inequalities in access to services across a range of sectors (e.g. health, energy, housing) to ensure fairness in AI. We use latent class analysis to measure cross-sectoral inequalities between user-defined groups, and analyse inequalities across different ethnic groups using UK EVENS and census data. We verify the reliability of the measured inequalities through correlation analysis with government public indicators, and find significant inequalities between ethnic minority groups and between ethnic minority and non-ethnic minority groups, highlighting the need for targeted interventions in policy-making. We also show that the proposed approach can provide valuable insights into ensuring fairness in machine learning systems.