  We use high-resolution data from the millimetre-Wave Interferometric Survey
of Dark Object Masses (WISDOM) project to investigate the connection between
circumnuclear gas reservoirs and nuclear activity in a sample of nearby
galaxies. Our sample spans a wide range of nuclear activity types including
radio galaxies, Seyfert galaxies, low-luminosity active galactic nuclei (AGN)
and inactive galaxies. We use measurements of nuclear millimetre continuum
emission along with other archival tracers of AGN accretion/activity to
investigate previous claims that at, circumnuclear scales (<100 pc), these
should correlate with the mass of the cold molecular gas. We find that the
molecular gas mass does not correlate with any tracer of nuclear activity. This
suggests the level of nuclear activity cannot solely be regulated by the amount
of cold gas around the supermassive black hole (SMBH). This indicates that AGN
fuelling, that drives gas from the large scale galaxy to the nuclear regions,
is not a ubiquitous process and may vary between AGN type, with timescale
variations likely to be very important. By studying the structure of the
central molecular gas reservoirs, we find our galaxies have a range of nuclear
molecular gas concentrations. This could indicate that some of our galaxies may
have had their circumnuclear regions impacted by AGN feedback, even though they
currently have low nuclear activity. On the other hand, the nuclear molecular
gas concentrations in our galaxies could instead be set by secular processes.
