We investigate the effect of oil price shocks on UK inflation using a time‐varying vector autoregression with stochastic volatility. The estimates show that the oil price–inflation pass‐through declined from the early 1980s until the mid/late 1990s. Post‐2003, however, the importance of oil price shocks for UK inflation rose significantly. The rise in the pass‐through coincided with a significant increase in the size of oil price shocks. This paper shows that allowing for time variation in the stochastic volatilities better captures time variation between oil prices and UK inflation.