The modulational instability that occurs during the interaction of a long laser pulse and its own wakefield in an underdense plasma has been studied experimentally and theoretically. Recent experiments using laser pulses that are several times longer than the wakefield period have yielded transmission spectra that exhibit a series of secondary peaks flanking the main laser peak. These peaks are too closely spaced to be the result of Raman instabilities; their origin was found to be photon acceleration of the laser's photons in the wakefield instead. In the experiments described in this paper, a laser pulse of 50–200 fs containing 300–600 mJ was focused on the edge of a helium gas jet on a 25 µm focal spot. The observed transmission spectra show evidence of both ionization blueshift and modulation by the pulse's wakefield. The transmission spectra have also been modelled using a dedicated photon-kinetic numerical code. The modelling has revealed a direct correlation between the spectral modulations and the amplitude of the excited wakefield. By comparing the measured and simulating spectra, the origin of various spectral characteristics has been explained in terms of photon acceleration. The feasibility of using this effect as a wakefield diagnostic will be discussed.