The ability to form images through hair-thin optical fibres promises to open up new applications from biomedical imaging to industrial inspection. Unfortunately, their deployment has been limited because small changes in mechanical deformation (e.g. bending) and temperature can completely scramble optical information, which distorts the resulting images. Since such changes are dynamic, correcting them requires measurement of the fibre transmission matrix in situ immediately before imaging. Transmission matrix calibration typically requires access to both the proximal and distal facets of the fibre simultaneously, which 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 transmission matrix of multi-mode or multi-core optical fibre in a reflection-mode configuration without requiring access to the distal facet. A thin stack of structured metasurface reflectors is used at the distal facet of the fibre to introduce wavelength-dependent, spatially heterogeneous reflectance profiles. We derive a first-order fibre model that compensates these wavelength-dependent changes in the fibre transmission matrix and show that, consequently, the reflected data at 3 wavelengths can be used to unambiguously reconstruct the full transmission matrix by an iterative optimisation algorithm. We then present a method for sample illumination and imaging following reconstruction of the transmission matrix. Unlike previous approaches, our method does not require the fibre matrix to be unitary making it applicable to physically realistic fibre systems that have non-negligible power loss. We demonstrate the transmission matrix reconstruction and imaging method first using simulated non-unitary fibres and noisy reflection matrices, then using much larger experimentally-measured transmission matrices of a densely-packed multicore fibre. Finally, we demonstrate the method on an experimentally-measured multi-wavelength set of transmission matrices recorded from a step-index multimode fibre. Our findings pave the way for online transmission matrix calibration in situ in hair-thin optical fibres.