We have carried out Hubble Space Telescope (HST) snapshot observations at 1.1 μm of 281 candidate strongly lensed galaxies identified in the wide-area extragalactic surveys conducted with the Herschel Space Observatory. Our candidates comprise systems with flux densities at 500 μm, S₅₀₀ ≥ 80 mJy. We model and subtract the surface brightness distribution for 130 systems, where we identify a candidate for the foreground lens candidate. After combining visual inspection, archival high-resolution observations, and lens subtraction, we divide the systems into different classes according to their lensing likelihood. We confirm 65 systems to be lensed. Of these, 30 are new discoveries. We successfully perform lens modelling and source reconstruction on 23 systems, where the foreground lenses are isolated galaxies and the background sources are detected in the HST images. All the systems are successfully modelled as a singular isothermal ellipsoid. The Einstein radii of the lenses and the magnifications of the background sources are consistent with previous studies. However, the background source circularized radii (between 0.34 and 1.30 kpc) are ∼3 times smaller than the ones measured in the sub-millimetre/millimetre for a similarly selected and partially overlapping sample. We compare our lenses with those in the Sloan Lens Advanced Camera for Surveys (ACS) Survey confirming that our lens-independent selection is more effective at picking up fainter and diffuse galaxies and group lenses. This sample represents the first step towards characterizing the near-infrared properties and stellar masses of the gravitationally lensed dusty star-forming galaxies.