We estimate the effect of the introduction of the UK's National Living Wage in 2016, and increases in it up to 2019, using a new empirical method. We apply a bunching approach to a setting with no geographical variation in minimum wage rates. We effectively compare employment changes in each part of the wage distribution in low-wage areas to employment changes among similar workers living in higher-wage areas who are less exposed to increases in the national minimum wage because their nominal wages are further above it. We find substantial positive wage effects, including statistically significant spillovers up to around the 20th percentile of wages. Overall we find small negative effects on employment which are not statistically significant. We combine these estimates with a tax and benefit microsimulation model to estimate the impact on household incomes. The largest gains go to the middle of the overall working-age income distribution, though they are more concentrated within the bottom third if we consider only households with someone in paid work. The gains to poorer working households are limited by the withdrawal of means tested benefits as earnings increase. Effects of minimum wages on household incomes are very sensitive to the size of employment effects.