Quasar damped Ly{alpha} (DLA) absorption-line systems with redshifts z<1.65 are used to trace neutral gas over approximately 70 percent of the most recent history of the Universe. However, such systems fall in the UV and are rarely found in blind UV spectroscopic surveys. Therefore, it has been difficult to compile a moderate-sized sample of UV DLAs in any narrow cosmic time interval. However, DLAs are easy to identify in low-resolution spectra because they have large absorption rest equivalent widths. We have performed an efficient strong-Mg ii-selected survey for UV DLAs at redshifts z=[0.42,0.70] using Hubble Space Telescope's low-resolution ACS-HRC-PR200L prism. This redshift interval covers ~1.8Gyr in cosmic time, i.e. t~[7.2,9.0]Gyr after the big bang. A total of 96 strong MgII absorption-line systems identified in Sloan Digital Sky Survey spectra were successfully observed with the prism at the predicted UV wavelengths of Ly{alpha} absorption. We found that 35 of the 96 systems had a significant probability of being DLAs. One additional observed system could be a very high N_HI_ DLA (N_HI_~2x10^22^atoms/cm^2^ or possibly higher), but since very high N_HI_ systems are extremely rare, it would be unusual for this system to be a DLA given the size of our sample. Here we present information on our prism sample, including our best estimates of N_HI_ and errors for the 36 systems fitted with DLA profiles. This list is valuable for future follow-up studies of low-redshift DLAs in a small redshift interval, although such work would clearly benefit from improved UV spectroscopy to more accurately determine their neutral hydrogen column densities.