In low scale quantum gravity scenarios the fundamental scale of nature can be as low as 1 TeV, in order to address the naturalness of the electroweak scale. A number of difficulties arise in constructing specific models: stabilization of the radius of the extra dimensions, avoidance of overproduction of Kaluza-Klein modes, achieving successful baryogenesis and production of a close to scale-invariant spectrum of density perturbations with the correct amplitude. We examine in detail the dynamics, including radion stabilization, of a hybrid inflation model that has been proposed in order to address these difficulties, where the inflaton is a gauge singlet residing in the bulk. We find that for a low fundamental scale the phase transition, which in standard four dimensional hybrid models usually ends inflation, is slow and there is a second phase of inflation lasting for a large number of e-foldings. The density perturbations on cosmologically interesting scales exit the Hubble radius during this second phase of inflation, and we find that their amplitude is far smaller than is required. We find that the duration of the second phase of inflation can be short, so that cosmologically interesting scales exit the Hubble radius prior to the phase transition, and the density perturbations have the correct amplitude, only if the fundamental scale takes an intermediate value. Finally we comment briefly on the implications of an intermediate fundamental scale for the production of primordial black holes and baryogenesis.