Magnetic massive stars are stars of spectral types O, B and A that harbour ∼ kG strength (mostly dipolar) surface magnetic fields. Their non-thermal radio emission has been demonstrated to be an important magnetospheric probe, provided the emission is fully characterised. A necessary step for that is to build a statistically significant sample of radio-bright magnetic massive stars. In this paper, we present the ‘VAST project to study Magnetic Massive Stars’ or VAST-MeMeS that aims to achieve that by taking advantage of survey data acquired with the Australian SKA Pathfinder telescope. VAST-MeMeS is defined under the ‘Variables and Slow Transients’ (VAST) survey, although it also uses data from other ASKAP surveys. We found radio detections from 48 magnetic massive stars, out of which, 14 do not have any prior radio detections. We also identified 9 ‘Main-sequence Radio Pulse Emitter’ candidates based on variability and circular polarisation of flux densities. The expanded sample suggests a slightly lower efficiency in the radio production than that reported in earlier work. In addition to significantly expanding the sample of radio-bright magnetic massive stars, the addition of flux density measurements at ≲ 1 GHz revealed that the spectra of incoherent radio emission can extend to much lower frequencies than that assumed in the past. In the future, radio observations spanning wide frequency and rotational phase ranges should be conducted so as to reduce the uncertainties in the incoherent radio luminosities. The results from these campaigns, supplemented with precise estimations of stellar parameters, will allow us to fully understand particle acceleration and non-thermal radio production in large-scale stellar magnetospheres.