ABSTRACT We report an ASKAP search for associated H i 21-cm absorption against bright radio sources from the Molonglo Reference Catalogue (MRC) 1-Jy sample. The search uses pilot survey data from the ASKAP First Large Absorption Survey in H i (FLASH) covering the redshift range 0.42 < z < 1.00. From a sample of 62 MRC 1-Jy radio galaxies and quasars, we report three new detections of associated H i 21-cm absorption, yielding an overall detection fraction of $1.8\,{{\,\rm per\,cent}}^{+4.0\,{{\,\rm per\,cent}}}_{-1.5\,{{\,\rm per\,cent}}}$. The detected systems comprise two radio galaxies (MRC 2216−281 at z = 0.657 and MRC 0531−237 at z = 0.851) and one quasar (MRC 2156−245 at z = 0.862). The MRC 0531−237 absorption system is the strongest found to date, with a velocity integrated optical depth of $\rm 143.8 ± 0.4 \ km \ s^{-1}$. All three objects with detected H i 21-cm absorption are peaked-spectrum or compact steep-spectrum (CSS) radio sources. Two of them show strong interplanetary scintillation at 162 MHz, implying that the radio continuum source is smaller than 1 arcsec in size even at low frequencies. Among the class of peaked-spectrum and compact steep-spectrum radio sources, the H i detection fraction is $23\,{{\,\rm per\,cent}}^{+22\,{{\,\rm per\,cent}}}_{-13\,{{\,\rm per\,cent}}}$. All three detections have a high 1.4 GHz radio luminosity, with MRC 0531−237 and MRC 2216−281 having the highest values in the sample, $\rm \gt 27.5 \ W \ Hz^{-1}$. The preponderance of extended radio sources in our sample could partially explain the overall low detection fraction, while the effects of a redshift evolution in gas properties and AGN UV luminosity on the neutral gas absorption still need to be investigated.