Measurements of the double-differential π± production cross-section in the range of momentum 100 MeV/c≤p< 800 MeV/c and angle 0.35 rad ≤θ<  2.15 rad in proton–beryllium, proton–aluminium and proton–lead collisions are presented. The data were taken with the HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 GeV/c to 12.9 GeV/c hitting a target with a thickness of 5% of a nuclear interaction length. The tracking and identification of the produced particles was performed using a small-radius cylindrical time projection chamber (TPC) placed inside a solenoidal magnet. Incident particles were identified by an elaborate system of beam detectors. Results are obtained for the double-differential cross-sections d2σ/dpdθ at six incident proton beam momenta (3 GeV/c, 5 GeV/c, 8 GeV/c, 8.9 GeV/c (Be only), 12 GeV/c and 12.9 GeV/c (Al only)) and compared to previously available data.