We present far-infrared (FIR) and submillimetre photometry from the Herschel Space Observatory's Spectral and Photometric Imaging Receiver (SPIRE) for 313 nearby ( z 〈 0.05) active galactic nuclei (AGN). We selected AGN from the 58 month Swift Burst Alert Telescope (BAT) catalogue, the result of an all-sky survey in the 14–195 keV energy band, allowing for a reduction in AGN selection effects due to obscuration and host galaxy contamination. We find 46 per cent (143/313) of our sample is detected at all three wavebands and combined with our Photoconductor Array Camera and Spectrometer (PACS) observations represents the most complete FIR spectral energy distributions of local, moderate-luminosity AGN. We find no correlation among the 250, 350, and 500 μm luminosities with 14–195 keV luminosity, indicating the bulk of the FIR emission is not related to the AGN. However, Seyfert 1s do show a very weak correlation with X-ray luminosity compared to Seyfert 2s and we discuss possible explanations. We compare the SPIRE colours ( F 250 / F 350 and F 350 / F 500 ) to a sample of normal star-forming galaxies, finding the two samples are statistically similar, especially after matching in stellar mass. But a colour–colour plot reveals a fraction of the Herschel -BAT AGN are displaced from the normal star-forming galaxies due to excess 500 μm emission ( E 500 ). Our analysis shows E 500 is strongly correlated with the 14–195 keV luminosity and 3.4/4.6 μm flux ratio, evidence the excess is related to the AGN. We speculate these sources are experiencing millimetre excess emission originating in the corona of the accretion disc.