We report a highly significant (> 10 ) spatial correlation between galaxies with S350μm > 30mJy detected in the equatorial fields of the Herschel Astrophysical Ter- ahertz Large Area Survey (H-ATLAS) with estimated redshifts & 1.5, and SDSS or GAMA galaxies at 0.2 6 z 6 0.6. The significance of the cross-correlation is much higher than those reported so far for samples with non-overlapping redshift distribu- tions selected in other wavebands. Extensive, realistic simulations of clustered sub-mm galaxies amplified by foreground structures confirm that the cross-correlation can be explained by weak gravitational lensing (μ < 2). The simulations also show that the measured amplitude and range of angular scales of the signal are larger than can be ac- counted for by galaxy-galaxy weak lensing. However, for scales . 2 arcmin, the signal can be reproduced if SDSS/GAMA galaxies act as signposts of galaxy groups/clusters with halo masses in the range 1013.2–1014.5M⊙. The signal detected on larger scales appears to reflect the clustering of such halos.