The ability to retrieve image data through hair-thin optical fibres promises to open up new applications in a range of fields, from biomedical imaging to industrial inspection. Unfortunately, small changes in mechanical deformation and temperature can completely scramble optical information, distorting any resulting images. Correction of these dynamic changes requires measurement of the fi bre transmission matrix (TM) in situ immediately before imaging, which typically requires access to both the proximal and distal facets of the fibre simultaneously. As a result, TM calibration is not feasible during most realistic usage scenarios without compromising the thin form factor with bulky distal optics. Here, we introduce a new approach to determine the TM of multi-mode or multi-core optical fibres in a reflection-mode con figuration, without requiring access to the distal facet. We propose to introduce a thin stack of structured metasurface reflectors at the distal facet of the fi bre, to introduce wavelength-dependent, spatially heterogeneous reflectance profi les. We derive a first-order fibre model that compensates these wavelength-dependent changes in the fi bre TM and show that, consequently, the reflected data at three wavelengths can be used to unambiguously reconstruct the full TM by an iterative optimisation algorithm. Unlike previous approaches, our method does not require the fi bre matrix to be unitary, making it applicable to physically realistic fibre systems that have non-negligible power loss. We demonstrate TM reconstruction and imaging fi rst using simulated non-unitary fibres and noisy reflection matrices, then using larger experimentally-measured TMs of a densely-packed multi-core fibre (MCF), and finally using experimentally-measured multi-wavelength TMs recorded from a step-index multimode fibre (MMF). Parallelisation of multi-wavelength in situ measurements could enable experimental characterisation times comparable with state-of-the-art transmission-mode fibre TM experiments. Our findings pave the way for online TM calibration in situ in hair-thin optical fibres.