In this paper we model the income distribution using a Bayesian approach and a mixture of lognormal densities. The size of the mixture is determined by Chib (1995)’s method. Using the Federal Expenditure Survey data for the United Kingdom, we detect three groups corresponding to the three classes (poor, middle class and rich). The marked growth in UK income inequality during the late 1970s is in- creasingly attracting attention. The increasing gap between the poorest and the richest was accompanied by changes in the clustering of incomes in be- tween. Using the decomposable Generalised Entropy (GE) inequality indices, we carry out a within-between group analysis of income inequality in the three identified groups in UK during 1979 to 1996 and show the evolution of the importance of each group. Whereas during the late 1970s the concentration of people around middle income levels began to break up and polarise towards high and low incomes as shown by Jenkins (1996), our Bayesian results show that the inequality within the low and middle income group do not change much and the importance of the high income is the most affected by the fight against inequality that followed the Thatcher period.