Polymeric fibres with small radii (such as ≤125 nm) are delicate to handle and should be laid down on a solid substrate to obtain practical devices. However, placing these nanofibres on commonly used glass substrates prevents them from guiding light. In this study, we numerically and experimentally demonstrate that when the nanofibre is placed on a suitable dielectric multilayer, it supports a guided mode, a Bloch surface wave (BSW) confined in one dimension. The physical origin of this new mode is discussed in comparison with the typical two-dimensional BSW mode. Polymeric nanofibres are easily fabricated to contain fluorophores, which make the dielectric nanofibre and multilayer configuration suitable for developing a large range of new nanometric scale devices, such as processor-memory interconnections, devices with sensitivity to target analytes, incident polarization and multi-colour BSW modes.