We apply coaxial electrospinning to produce core-sheath polymer composite fibres with encapsulated short-pitch cholesteric liquid crystal, giving the fibres iridescent colours due to selective reflection within a narrow band of the visible wavelength spectrum. By modifying the feed rate of the liquid crystal during spinning we can tune the fibre diameter from the sub-micron range to about 7 mm, other ranges being accessible via further modifications of the spinning parameters. We demonstrate that the thinnest fibres display quantised colours, determined primarily by the core diameter, whereas the thicker fibres allow a quasi-continuous change in colour if the cholesteric helix pitch changes. Because of the strong response function of liquid crystals, phases as well as structures changing in response to small changes in the environment, the resulting non-woven fibre mats have potential for smart textiles, in particular in sensing applications.