This paper uses a time-varying Factor Augmented VAR to investigate the evolving transmission of monetary policy and demand shocks in the UK. Simultaneous estimation of time-varying impulse responses of a large set of macroeconomic variables and disaggregated prices suggest that the response of inflation, money supply and asset prices to monetary policy and demand shocks has changed over the sample period. In particular, during the post-1992 inflation targeting period, monetary policy shocks started having a bigger impact on prices, a smaller impact on activity and began contributing more to overall volatility. In contrast, demand shocks had the largest impact on these variables before the 1990s. We also document changes in the response of disaggregated prices, with the median reaction to contractionary policy shocks becoming more negative and the distribution more dispersed post-1992.