Recent experiments in the Joint European Torus (JET) have provided evidence of sawtooth stabilization by fast ions arising from deuterium neutral beam injection (NBI). A possible theoretical basis for the interpretation of the observed sawtooth period behaviour is investigated and predictions are compared with experimental results, using a sawtooth period model developed to predict the sawtooth period in the International Thermonuclear Experimental Reactor (ITER). Unlike the case of ion cyclotron resonance heating, a detailed comparison between theory and experiment for NBI has not yet been made. In the model employed in this paper, a beam ion contribution to the internal kink potential energy has been incorporated, using a simple analytical expression valid in the limit of isotropic fast particles. This analytical expression has been found to compare well with detailed calculations performed with a hybrid kinetic/MHD code NOVA-K, using fast particle distribution functions computed with a plasma analysis code TRANSP. The beam ion contribution has been implemented in a transport code PRETOR and a few representative JET discharges have been analysed and modelled. The beam ion term is found to be sufficiently stabilizing to produce simulated sawtooth periods in agreement with the experimental results. Sawtooth periods computed without taking this term into account are much shorter than the measured periods. The model indicates that sawteeth are triggered in these JET discharges by excitation of the internal kink in the semi-collisional ion-kinetic regime: this was found by previous authors to be the sawtooth trigger most likely to be relevant to ITER. The role of beam ions in determining the sawtooth period in JET is thus found to be similar to the predicted role of alpha-particles in ITER.