Absolute and differential chemical abundances are presented for the largest group of massive stars in M 31 studied to date. These results were derived from intermediate resolution spectra of seven B-type supergiants, lying within four OB associations covering a galactocentric distance of 5-12 kpc. The results are mainly based on an LTE analysis, and we additionally present a full non-LTE, unified model atmosphere analysis of one star (OB 78-277) to demonstrate the reliability of the differential LTE technique. A comparison of the stellar oxygen abundance with that of previous nebular results shows that there is an offset of between ~ 0.15-0.4 dex between the two methods which is critically dependent on the empirical calibration adopted for the R_23 parameter with [O/H]. However within the typical errors of the stellar and nebular analyses (and given the strength of dependence of the nebular results on the calibration used) the oxygen abundances determined in each method are fairly consistent. We determine the radial oxygen abundance gradient from these stars, and do not detect any systematic gradient across this galactocentric range. We find that the inner regions of M 31 are not, as previously thought, very ``metal rich''. Our abundances of C, N, O, Mg, Si, Al, S and Fe in the M 31 supergiants are very similar to those of massive stars in the solar neighbourhood.