Because finite sample inference for inequality indices based on asymptotic methods or the standard bootstrap does not perform well, Davidson and Flachaire (Journal of Econometrics, 2007) and Cowell and Flachaire (Journal of Econometrics, 2007) proposed inference based on semiparametric methods in which the upper tail of incomes is modelled by a Pareto distribution. Using simulations, they argue accurate inference is achievable with moderately large samples. We provide the first systematic application of these and other inferential approaches to real-world income data (high-quality UK household survey data covering 1977–2018), while also modifying them to deal with weighted data and a large portfolio of inequality indices. We find that the semiparametric asymptotic approach provides a greater number of statistically significant differences than the semiparametric bootstrap which in turn provides more than the conventional asymptotic approach and the ‘Student-t’ approach (Ibragimov et al., Econometric Reviews, 2025), especially for year-pair comparisons within the period from the late-1980s onwards.