We study the properties of low-mass stars recently formed in the field of the NGC 376 cluster in the Small Magellanic Cloud (SMC). Using photometric observations acquired with the Hubble Space Telescope (HST) in the V, I, and H-alpha bands, we identify 244 candidate pre-main sequence (PMS) stars showing H-alpha excess emission at the 5-sigma level and with H-alpha equivalent width of 20{AA} or more. We derive physical parameters for all PMS stars, including masses, ages, and mass accretion rates. We compare the effective mass accretion rate of stars in NGC 376 to that of objects in the NGC 346 cluster, with NGC 346 featuring similar metallicity but higher total mass and gas density. We find a median age of 28Myr for this population (with 25th and 75th percentiles at about 20 and 40Myr, respectively), in excellent agreement with previous studies of massive stars in the same field. The PMS stars are rather uniformly distributed across the field, whereas massive stars are more clustered. The spatial distribution of PMS objects is compatible with them having formed in the centre of the cluster and then migrating outwards. We find that in NGC 376 the mass accretion rate is systematically lower than in NGC 346 for stars of the same mass and age. This indicates that, in addition to metallicity, there are other environmental factors affecting the rate of mass accretion onto PMS stars. Our observations suggest that the gas density in the star-forming region might play a role.