Cosmic magnification is due to the weak gravitational lensing of sources in the distant Universe by foreground large-scale structure leading to coherent changes in the observed number density of the background sources. Depending on the slope of the background source number counts, cosmic magnification causes a correlation between the background and foreground galaxies, which is unexpected in the absence of lensing if the two populations are spatially disjoint. Previous attempts using submillimetre (submm) sources have been hampered by small number statistics. The large number of sources detected in the Herschel Multi-tiered Extra-galactic Survey (HerMES) Lockman-Spitzer Wide-area Infrared Extragalactic (SWIRE) field enables us to carry out the first robust study of the cross-correlation between submm sources and sources at lower redshifts. Using ancillary data, we compile two low-redshift samples from Sloan Digital Sky Survey (SDSS) and SWIRE with ˜ 0.2 and 0.4, respectively, and cross-correlate with two submm samples based on flux density and colour criteria, selecting galaxies preferentially at z˜ 2. We detect cross-correlation on angular scales between ˜1 and 50 arcmin and find clear evidence that this is primarily due to cosmic magnification. A small, but non-negligible signal from intrinsic clustering is likely to be present due to the tails of the redshift distribution of the submm sources overlapping with those of the foreground samples. Herschel is a European Space Agency (ESA) space observatory with science instruments provided by European-led Principle Investigator consortia and with important participation from NASA.