We present the largest sample to-date of intermediate-resolution blue-to-red optical spectra of B-type supergiants in M31 and undertake the first survey of diffuse interstellar bands (DIBs) in this galaxy. Spectral classifications, radial velocities and interstellar reddenings are presented for 34 stars in three regions of M31. Radial velocities and equivalent widths are given for the 5780 and 6283 DIBs towards 11 stars. Equivalent widths are also presented for the following DIBs detected in three sightlines in M31: 4428, 5705, 5780, 5797, 6203, 6269, 6283, 6379, 6613, 6660, and 6993. All of these M31 DIB carriers reside in clouds at radial velocities matching those of interstellar Na I and/or H I. The relationships between DIB equivalent widths and reddening (E(B-V)) are consistent with those observed in the local ISM of the Milky Way. Many of the observed sightlines show DIB strengths (per unit reddening) which lie at the upper end of the range of Galactic values. DIB strengths per unit reddening are found (with 68% confidence), to correlate with the interstellar UV radiation field strength. The strongest DIBs are observed where the interstellar UV flux is lowest. The mean Spitzer 8/24 micron emission ratio in our three fields is slightly lower than that measured in the Milky Way, but we identify no correlation between this ratio and the DIB strengths in M31. Interstellar oxygen abundances derived from the spectra of three M31 H II regions in one of the fields indicate that the average metallicity of the ISM in that region is 12 + log[O/H] = 8.54 +- 0.18, which is approximately equal to the value in the solar neighbourhood.