Barely in the UK
Our results suggest that the overall effect of monetary policy on standard relative measures of income and wealth inequality has been small. Given the pre-existing disparities in income and wealth, we estimate that the impact on each household varied substantially across the income and wealth distributions in cash terms, but in percentage terms the effects were broadly similar. We estimate that households around retirement age gained the most from the support to wealth, but that support to incomes disproportionately benefited the young.

The distributional impact of monetary policy easing in the UK between 2008 and 2014
Authors: Philip Bunn, Alice Pugh, Chris Yeates
From: Bank of England
Negligibly in Italy
Larger benefits accrue to households at the bottom of the income scale, as the effects via the stimulus to economic activity and employment outweigh those via financial variables. The response of net wealth is U-shaped: less wealthy households take advantage of their leveraged positions, wealthier households of their larger share of financial assets. Overall, the effects on inequality are negligible.

A “reverse Robin Hood”? The distributional implications of non-standard monetary policy for Italian households
Authors: Marco Casiraghi, Eugenio Gaiotti, Lisa Rodano, Alessandro Secchi
From: Banca d’ Italia
Modestly in the US
The unavoidable conclusion from the detailed decomposition exercise and the counterfactual analysis carried out above is that the impact of quantitative easing on the distribution income was at least modestly regressive. Our decomposition results imply that the disequalizing effects of equity returns far outweighed the equalizing effects of employment gains. While these decomposition results cannot be interpreted causally, the counterfactual scenarios presented in the previous section suggest that, for reasonable assumptions about the employment effects of QE, the causal impact of QE on stock prices would have to be implausibly small for the net effect to be distributionally neutral. These dis-equalizing impacts were due to both policy choices and deep seated structural problems
Did Quantitative Easing Increase Income Inequality?
Authors: Juan Antonio Montecino, Gerald Epstein
From: University of Massachusetts at Amherst