The success of photonic crystal fibres relies largely on the endless variety of two-dimensional photonic crystals in the cross-section. Here, we propose a topological bandgap fibre whose bandgaps along in-plane directions are opened by generalised Kekulé modulation of a Dirac lattice with a vortex phase. Then, the existence of mid-gap defect modes is guaranteed to guide light at the core of this Dirac-vortex fibre, where the number of guiding modes equals the winding number of the spatial vortex. The single-vortex design provides a single-polarisation single-mode for a bandwidth as large as one octave.