Whispering gallery mode resonances in liquid droplets and microspheres have attracted considerable attention due to their potential uses in a range of sensing and technological applications. We describe a whispering gallery mode sensor in which standard optical fibre is used as the whispering gallery mode resonator. The sensor is characterised in terms of the response of the whispering gallery mode spectrum to changes in resonator size, refractive index of the surrounding medium, and temperature, and its measurement capabilities are demonstrated through application to high-precision fibre geometry profiling and the detection of unlabelled biochemical species. The prototype sensor is capable of detecting unlabelled biomolecular species in attomole quantities.