The generation of large multiphoton quantum states-for applications in computing, metrology and simulation-requires a network of highefficiency quantum memories capable of storing broadband pulses. Integrating these memories into a fibre offers a number of advantages towards realizing this goal: strong light-matter coupling at low powers, simplified alignment and compatibility with existing photonic architectures. Here, we introduce a largecore kagome-structured hollow-core fibre as a suitable platform for an integrated fibre-based quantum memory with a warm atomic vapour. We demonstrate, for the first time, efficient optical pumping in such a system, where 90 ± 1% of atoms are prepared in the ground state. We measure high optical depths (3 × 10 4 ) and narrow homogeneous linewidths (6 ± 2 MHz) that do not exhibit significant