Context. During the journey from the cloud to the disc, the chemical composition of the protostellar envelope material can be either preserved or processed to varying degrees depending on the surrounding physical environment. Aims. This works aims to constrain the interplay of solid (ice) and gaseous methanol (CH₃OH) in the outer regions of protostellar envelopes located in the Coronet cluster in Corona Australis (CrA), and assess the importance of irradiation by the Herbig Ae/Be star R CrA. CH₃OH is a prime test case as it predominantly forms as a consequence of the solid-gas interplay (hydrogenation of condensed CO molecules onto the grain surfaces) and it plays an important role in future complex molecular processing. Methods. We present 1.3 mm Submillimeter Array (SMA) and Atacama Pathfinder Experiment (APEX) observations towards the envelopes of four low-mass protostars in the Coronet cluster. Eighteen molecular transitions of seven species were identified. We calculated CH₃OH gas-to-ice ratios in this strongly irradiated cluster and compared them with ratios determined towards protostars located in less irradiated regions such as Serpens SVS 4 in Serpens Main and the Barnard 35A cloud in the λ Orionis region. Results. The CH₃OH gas-to-ice ratios in the Coronet cluster vary by one order of magnitude (from 1.2 × 10⁻⁴ to 3.1 × 10⁻³) which is similar to less irradiated regions as found in previous studies. We find that the CH₃OH gas-to-ice ratios estimated in these three regions are remarkably similar despite the different UV radiation field intensities and formation histories. Conclusions. This result suggests that the overall CH₃OH chemistry in the outer regions of low-mass envelopes is relatively independent of variations in the physical conditions and hence that it is set during the prestellar stage.