This paper proposes an approach for lateral force sensing based on fibre Bragg gratings (FBGs) and Gaussian process regression (GPR). The monitoring system is based on FBG sensors embedded in a glass structure (load cell), which converts the external lateral force into axial strain along the fibre. Whilst the use of conventional peak detection techniques to retrieve the Bragg wavelength of the embedded FBG sensor can easily fail due to the FBG spectral distortions induced by the lateral force, the proposed GPR approach permits a direct mapping of the FBG spectral shape (including its peak wavelength and any observed distortion) into the applied lateral force. Experimental results validate the proposed approach, demonstrating highly accurate lateral force monitoring even in conditions with distorted FBG reflection spectra.