We investigate the possibility that the Universe may inflate due to moduli fields, corresponding to flat directions of supersymmetry, lifted by supergravity corrections. Using a hybrid-type potential we obtain a two-stage inflationary model. Depending on the curvature of the potential, the first stage corresponds to a period of fast-roll inflation or a period of 'locked' inflation, induced by an oscillating inflaton. This is followed by a second stage of fast-roll inflation. We demonstrate that these two consecutive inflationary phases result in enough total e-foldings to encompass the cosmological scales. Using natural values for the parameters (masses of order TeV and vacuum energy of the intermediate scale corresponding to gravity mediated supersymmetry breaking) we conclude that the η-problem of inflation is easily overcome. The greatest obstacle to our scenario is the possibility of copious production of cosmologically disastrous primordial black holes due to the phase transition switching from the first into the second stage of inflation. We study this problem in detail and show analytically that there is ample parameter space where these black holes do not form at all. To generate structure in the Universe we assume the presence of a curvaton field. Finally we also discuss the moduli problem and how it affects our considerations.