In April 2016, a National Living Wage replaced the National Minimum Wage for employees in the UK aged 25 and above, raising their statutory wage floor by 50 pence per hour. This uprating was almost double any in the previous decade and expanded the share of jobs covered by the wage floor by around 50%. Using linked employer-employee data, we examine the effect of this policy on the propensity for minimum-wage employees to change firms. We find no evidence that the substantial compression at the bottom of the wage distribution affected the average rates of year-to-year cross-firm mobility among low-paid workers. While past studies have suggested relatively benign effects of UK minimum wage policy on employment levels, our findings suggest that this also applies to employment dynamics and the aggregate reallocation of workers across firms.