The potential of a fibre luminescent solar concentrator has been explored by means of both analytical and ray-tracing techniques. Coated fibres have been found to be more efficient than homogeneously doped fibres, at low absorption. For practical fibres concentration is predicted to be linear with fibre length. A 1 m long, radius 1 mm, fibre LSC doped with Lumogen Red 305 is predicted to concentrate the AM1.5 g spectrum up to 1100 nm at normal incidence by ~35 x. The collection efficiency under diffuse and direct irradiance in London has been analysed showing that, even under clear sky conditions, in winter the diffuse contribution equals the direct.