Productivity growth in the UK has been puzzlingly weak in recent years. By contrast, US productivity growth has been relatively robust at higher levels. There is a macroeconomic literature, however, that suggests that countries with lower levels of productivity should grow more quickly than high productivity countries. I argue that there is evidence of the UK catching up with the US in the past, but this relationship appears to have broken down after the financial crisis. If the past relationship between US and UK productivity returns, the prospects for UK productivity could be bright. But this improvement is likely to take time and will depend on fundamental drivers of productivity, like investment, R&D spending and educational attainment.