Using the Boolardy Engineering Test Array of the Australian Square Kilometre Array Pathfinder (ASKAP BETA), we have carried out the first $z = 0 - 1$ survey for HI and OH absorption towards the gravitationally lensed quasars PKSB1830$-$211 and MGJ0414$+$0534. Although we detected all previously reported intervening systems towards PKSB1830$-$211, in the case of MGJ0414+0534 three systems were not found, indicating that the original identifications may have been confused with radio frequency interference. Given the sensitivity of our data, we find that our detection yield is consistent with the expected frequency of intervening HI systems estimated from previous surveys for 21-cm emission in nearby galaxies and $z sim 3$ damped Lyman $alpha$ absorbers. We find spectral variability in the $z = 0.886$ face-on spiral galaxy towards PKSB1830$-$211, from observations undertaken with the Westerbork Synthesis Radio Telescope in 1997/1998 and ASKAP BETA in 2014/2015. The HI equivalent width varies by a few per cent over approximately yearly time-scales. This long-term spectral variability is correlated between the north-east and south-west images of the core, and with the total flux density of the source, implying that it is observationally coupled to intrinsic changes in the quasar. The absence of any detectable variability in the ratio of HI associated with the two core images is in stark contrast to the behaviour previously seen in the molecular lines. We therefore infer that coherent opaque HI structures in this galaxy are larger than the parsec-scale molecular clouds found at mm-wavelengths.