This work describes a new technique for fibre Bragg grating (FBG)sensor interrogation and multiplexing. The technique combines a scanningFabry-Perot (SFP) bandpass filter used to wavelength-multiplex multiplegratings in a single fibre, and an unbalanced Mach-Zehnder fibreinterferometer made with a 3×3 coupler to detect strain-inducedwavelength shifts. A passive technique for interferometer drift compensationusing non-sensing FBGs is included in the system. A prototype complete systeminterrogates four gratings in a single fibre at a Nyquist sampling rate up to10 kHz, with a noise floor measured near 4 nϵ Hz-1/2 above0.1 Hz. The inclusion of the interferometer drift compensation technique isshown to make quasi-static measurements feasible.