We have observed 104 gravitationally-lensed active galactic nuclei (AGN) at z ∼ 1–4 with Herschel/SPIRE, the largest such sample ever studied. By targeting gravitational lenses, we probe intrinsic far-infrared (FIR) luminosities and star formation rates (SFRs) more typical of the population than the extremely luminous sources that are otherwise accessible. We detect 71 percent (74 sources) of the sample, of which 66 percent (69 sources) have spectral energy distributions (SEDs) that are characteristic of heated dust emission. For objects with sufficiently constrained SEDs, we find a median modified black body dust temperature of 38+12 −5 K. We derive a median magnification-corrected FIR luminosity of 3.7 +4.9 −2.4 ×1011 L and a median SFR of 110+160 −70 M yr−1
for the sample. By applying the radio–infrared correlation, we find no evidence or an FIR excess which, in addition to the low dust temperatures, is consistent with dust heating that is dominated by star formation. These results are in line with
current models of quasar evolution, but suggest that most quasars exist in a transitional phase between a dusty star-forming galaxy and an AGN-dominated system. Synchrotron emission is found to dominate at FIR wavelengths for < 15 percent of those sources classified as powerful radio galaxies from cm-wavelength observations. We find the FIR luminosities of radio-bright quasars are lower on average, however further investigation of individual objects is required to correct for systematic biases.