We present submillimetre molecular line observations Of comet P/Swift-Tuttle (1192t = 1992 XXVIII) which were undertaken on 7 and 8 December 1992 with the James Clerk Maxwell Telescope (JCMT). Three molecules were detected. (1) HCN through its J (4-3) rotational line at 354.505 GHz; (2) H2CO through its 5(15)-4(14) ortho line-at 351.769 GHz and (3) CH3OH through several of its J (7-6) transitions at 338 GHz and one line at 341 GHz. The lines are blueshifted with. respect to the comet rest, velocity, which is indicative of preferential outgassing towards the Sun. The relative intensities of the CH3OH rotational lines show that the population distribution can,be described by a rotational temperature Of 45 +/- K, although deviations from thermal equilibrium are present. The comparison with an out-of-equilibrium model suggests that the collisional region where thermalization occurs is larger than is expected in an isotropic coma where neutral(neutral collisions prevail. The model is able to reproduce most of the observed methanol line intensities. From these observations, we derive production rates of Q(HCN) - 1.3 x 10(27) s(-1), Q(H2CO) = 5 x 10(27) s(-1) and Q(CH3OH) = 2 x 10(28) s(-1), assuming direct release from the nucleus and isotropic sublimation This corresponds to molecular abundances with respect to water of 0.3, 1 and 4%, for HCN, H2CO and CH3OH, respectively.