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We present a new set of solar metallicity atmosphere and evolutionary models for very cool brown dwarfs and self-luminous giant exoplanets, which we term ATMO 2020. Atmosphere models are generated with our state-of-the-art 1D radiative-convective equilibrium code ATMO, and are used as surface boundary conditions to calculate the interior structure and evolution of $0.001-0.075\,\mathrm{M_{\odot}}$ objects. Our models include several key improvements to the input physics used in previous models available in the literature. Most notably, the use of a new H-He equation of state including ab initio quantum molecular dynamics calculations has raised the mass by $\sim1-2\%$ at the stellar-substellar boundary and has altered the cooling tracks around the hydrogen and deuterium burning minimum masses. A second key improvement concerns updated molecular opacities in our atmosphere model ATMO, which now contains significantly more line transitions required to accurately capture the opacity in these hot atmospheres. This leads to warmer atmospheric temperature structures, further changing the cooling curves and predicted emission spectra of substellar objects. We present significant improvement for the treatment of the collisionally broadened potassium resonance doublet, and highlight the importance of these lines in shaping the red-optical and near-infrared spectrum of brown dwarfs. We generate three different grids of model simulations, one using equilibrium chemistry and two using non-equilibrium chemistry due to vertical mixing, all three computed self-consistently with the pressure-temperature structure of the atmosphere. We show the impact of vertical mixing on emission spectra and in colour-magnitude diagrams, highlighting how the $3.5-5.5\,\mathrm{μm}$ flux window can be used to calibrate vertical mixing in cool T-Y spectral type objects.