This work presents an extensive, comparative study of the gamma and electron radiation effects on the behaviour of femtosecond laser-inscribed fibre Bragg gratings (FBGs) using the point-by-point and plane-by-plane inscription methods. The FBGs were inscribed in standard telecommunication single mode silica fibre (SMF28) and exposed to a total accumulated radiation dose of 15 kGy for both gamma and electron radiation. The gratings’ spectra were measured and analysed before and after the exposure to radiation, with complementary material characterisation using Fourier transform infrared (FTIR) spectroscopy. Changes in the response of the FBGs’ temperature coefficients were analysed on exposure to the different types of radiation, and we consider which of the two inscription methods result in gratings that are more robust in such harsh environments. Moreover, we used the FTIR spectroscopy to locate which chemical bonds are responsible for the changes on temperature coefficients and which are related with the optical characteristics of the FBGs.