The Consumer Price Index (CPI) is a key economic statistic that informs various stakeholders, such as citizens, governments, about the recent past and future direction of inflation. Accurate inflation assessment and good forecasts are vital to understand, inform (e.g. internet charges or train fares that are tied to inflation indices) and control the economy, such as interest rate setting in central banks. The CPI averages various volume-weighted price indices of a basket of underlying component items taken from across the economy and is separately computed in very similar ways by the statistical offices of many countries. In the UK, the Bank of England has come in for criticism for its inflation forecasts, but the recent Bernanke 2024 review noted that `the forecast errors made by the Bank and those made by external forecasters are barely distinguishable.' Recently, it has been shown several times in the literature that generalised network autoregressive (GNAR) time series models have proved to be powerful forecasters in a variety of applied situations. We develop a technique (RaGNAR) to forecast monthly UK CPI using GNARs models by averaging forecasts obtained over many randomised networks and models, focussing on CPI as the objective. RaGNAR significantly outperforms both traditional benchmark and pre-trained probabilistic time series forecasting models across all horizons, and delivers materially more accurate forecasts than the Bank of England across four- to six-month horizons. This is somewhat surprising given the time-consuming and complex nature of the Bank’s forecasting process and the speed and efficiency of RaGNAR. Our methods also permit us to identify CPI components that most strongly influence the CPI during different periods.