The authors present optical excitation functions of singly excited helium states, measured by detecting the yield of emitted photons as a function of the incident electron energy from 56 to 66 eV. Many structures are observed, which are caused by negative-ion resonances and by the decay of autoionising states followed by post-collision interaction. Some of the structures are interpreted as being caused by hitherto unknown shape resonances lying very close to the thresholds of a particular class of autoionising states. As these shape resonances almost exclusively decay to their respective parent (autoionising) states, thereby considerably enhancing the threshold excitation cross sections of these states, they can only be observed via the PCI effect on the excitation functions of (higher lying) singly excited states. Using the recently introduced supermultiplet classification for doubly excited states a selection rule for the near-threshold excitation of doubly excited states by electron impact is deduced from the measurements.