  We revisit Starobinsky inflation in a quantum gravitational context, by means
of the exact Renormalisation Group (RG). We calculate the non-perturbative beta
functions for Newton's `constant' G and the dimensionless R^2 coupling, and
show that there exists an attractive UV fixed point where the latter one
vanishes but not the former one, and we provide the corresponding beta
functions. The smallness of the R^2 coupling, required for agreement with
inflationary observables, is naturally ensured by its vanishing at the UV fixed
point, ensuring the smallness of the primordial fluctuations, as well as
providing a theoretical motivation for the initial conditions needed for
successful inflation in this context. We discuss the corresponding RG dynamics,
showing both how inflationary and classical observations define the
renormalisation conditions for the couplings, and also how the UV regime is
connected with lower energies along the RG flow. Finally, we discuss the
consistency of our results when higher order curvature corrections are
included, and show that they are robust to the inclusion of R^3 corrections.
