  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. This works
aims to constrain the interplay of solid (ice) and gaseous methanol (CH$_3$OH)
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. CH$_3$OH 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. 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. Eighteen molecular transitions of seven
species are identified. We calculate CH$_3$OH gas-to-ice ratios in this
strongly irradiated cluster and compare them with ratios determined towards
protostars located in less irradiated regions such as the Serpens SVS 4 cluster
in Serpens Main and the Barnard 35A cloud in the $\lambda$ Orionis region. The
CH$_3$OH gas-to-ice ratios in the Coronet vary by one order of magnitude (from
1.2$\times$10$^{-4}$ to 3.1$\times$10$^{-3}$) which is similar to less
irradiated regions as found in previous studies. We find that the CH$_3$OH
gas-to-ice ratios estimated in these three regions are remarkably similar
despite the different UV radiation field intensities and formation histories.
This result suggests that the overall CH$_3$OH 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.
