It has been common practice in data assimilation to treat observation errors as uncorrelated; however, meteorological centres are beginning to use correlated inter-channel observation errors in their operational assimilation systems. In this work, we are the first to characterise inter-channel and spatial error correlations for Spinning Enhanced Visible and Infrared Imager (SEVIRI) observations that are assimilated into the Met Office high-resolution model. The errors are calculated using a diagnostic that calculates statistical averages of observation-minus-background and observation-minus-analysis residuals. This diagnostic is sensitive to the background and observation error statistics used in the assimilation, although, with careful interpretation of the results, it can still provide useful information. We find that the diagnosed SEVIRI error variances are as low as one-tenth of those currently used in the operational system. The water vapour channels have significantly correlated inter-channel errors, as do the surface channels. The surface channels have larger observation error variances and inter-channel correlations in coastal areas of the domain; this is the result of assimilating mixed pixel (land-sea) observations. The horizontal observation error correlations range between 30 km and 80 km, which is larger than the operational thinning distance of 24 km. We also find that estimates from the diagnostics are unaffected by biased observations, provided that the observation-minus-background and observation-minus-analysis residual means are subtracted.