Processing and distributing quantum information using photons through fibre-optic or free-space links is essential for building future quantum networks. The scalability needed for such networks can be achieved by employing photonic quantum states that are multiplexed into time and/or frequency, and light-matter interfaces that are able to store and process such states with large time-bandwidth product and multimode capacities. Despite important progress in developing such devices, the demonstration of these capabilities using non-classical light remains challenging. Employing the atomic frequency comb quantum memory protocol in a cryogenically cooled erbium-doped optical fibre, we report the quantum storage of heralded single photons at a telecom-wavelength (1.53 {mu}m) with a time-bandwidth product approaching 800. Furthermore we demonstrate frequency-multimode storage as well as memory-based spectral-temporal photon manipulation. Notably, our demonstrations rely on fully integrated quantum technologies operating at telecommunication wavelengths, i.e. a fibre-pigtailed nonlinear waveguide for the generation of heralded single photons, an erbium-doped fibre for photon storage and manipulation, and fibre interfaced superconducting nanowire devices for efficient single photon detection. With improved storage efficiency, our light-matter interface may become a useful tool in future quantum networks.