In this paper we study theoretically and experimentally a wavelength-tuneable Sagnac birefringence filter. The device is a Sagnac interferometer including a symmetric fibre coupler and a length of high birefringence fibre in the loop. A wave retarder is inserted at each end of the birefringent fibre for absolute wavelength tuning. We show theoretically that wavelength tuning through wave plate orientation ensuring constant amplitude of the filtering function is possible only if a minimum of two wave retarders are included in the setup. The position of the transmission peaks then varies linearly with the angle of one of the retarders and can be adjusted over one entire channel spacing. This happens only only when a quarter-wave retarder and a half-wave retarder are used, if the former is oriented at 45° with respect to the fibre birefringence axes, while the orientation of the latter serves as the adjustment parameter. The theoretical predictions are confirmed by the experimental results.