Polymer materials of reduced size and dimensionality, such as thin films, polymer nanofibres and nanotubes, exhibit exceptional mechanical properties compared with those of their macroscopic counterparts. We discuss here the abrupt increase in Young's modulus in polymer nanofibres. Using scaling estimation we show that this effect occurs when, in the amorphous (non-crystalline) part of the nanofibres, the transversal size of regions consisting of orientation-correlated macromolecules is comparable to the nanofibre diameter, thereby resulting in confinement of the supramolecular structure. We suggest that in polymer nanofibres the resulting supramolecular microstructure plays a more dominant role in the deformation process than previously thought, challenging the commonly held view that surface effects are most significant. The concept we develop also provides a way to interpret the observed--but not yet understood--temperature dependence of Young's modulus in nanofibres of different diameters.