  The leading order dynamics of the type IIB Large Volume Scenario is
characterised by the interplay between $\alpha'$ and non-perturbative effects
which fix the overall volume and all local blow-up modes leaving (in general)
several flat directions. In this paper we show that, in an arbitrary Calabi-Yau
with at least one blow-up mode resolving a point-like singularity, any
remaining flat directions can be lifted at subleading order by the inclusions
of higher derivative $\alpha'$ corrections. We then focus on simple fibred
cases with one remaining flat direction which can behave as an inflaton if its
potential is generated by both higher derivative $\alpha'$ and winding loop
corrections. Natural values of the underlying parameters give a spectral index
in agreement with observational data and a tensor-to-scalar ratio of order
$r=0.01$ which could be observed by forthcoming CMB experiments. Dangerous
corrections from higher dimensional operators are suppressed due to the
presence of an approximate non-compact shift symmetry.
