Nationally and internationally, universities are ranked in university league tables (ULTs). Sustained academic criticism of the rationale and methodology of compiling ULTs has not stopped these rankings exerting considerable pressure on the decisions of university managers. The compilation of ULTs is an inherently political act, with the choice and weighting of metrics resulting in particular characteristics of individual institutions being rewarded or penalised. One aspect that is currently not considered by league tables is the diversity of the student intake, and the extent to which an institution has been successful in "widening participation" (WP) in higher education (HE). The need to take action is reflected in target 4.3 of the fourth United Nations Sustainable Development Goal (SDG 4), which aims to "ensure equal access for all women and men to affordable and quality technical, vocational and tertiary education, including university" by 2030. This article explores how current ULT metrics for universities in the United Kingdom (UK) relate to WP. Using publicly available data, the authors found that over 75% of UK league table metrics are negatively related to WP. This has the effect of making institutions with a diverse student body significantly more likely to be lower down in the league tables. The worst relationship with WP is for entry standards. Universities which recruit high-performing students are actively rewarded in the league tables; this fails to recognise that students with high entry grades are more likely to come from privileged backgrounds. The authors developed a ULT which includes a WP score as an explicit league table metric and found that their WP-adjusted table removed the negative relationship between WP and league table rank, resulting in a somewhat fairer comparison between universities. They conclude that ULT compilers have an ethical duty to improve their definition of a "good" university, which in the current HE environment of the UK must include WP. The authors believe this should be an urgent priority for the sector, so that universities with a commitment to widening participation can be recognised and rewarded.