We present a deep, new 1200-mum survey of the ELAIS N2 and Lockman Hole fields using the Max-Planck Millimeter Bolometer array (MAMBO). The areas surveyed are 160 arcmin(2) in ELAIS N2 and 197 arcmin(2) in the Lockman Hole, covering the entire Submillimetre Common User Bolometer Array (SCUBA) 8-mJy survey. In total, 27 (44) sources have been detected at a significance greater than or equal to4.0sigma (greater than or equal to3.5sigma). The primary goals of the survey were to investigate the reliability of (sub) millimetre galaxy (SMG) samples, to analyse SMGs using flux ratios sensitive to redshift at z>3, and to search for 'SCUBA drop-outs', i.e. galaxies at zmuch greater than3. We present the 1200-mum number counts and find tentative evidence of a fall at bright flux levels. Employing parametric models for the evolution of the local 60-mum IRAS luminosity function, we are able to account simultaneously for the 1200- and 850-mum counts, suggesting that the MAMBO and SCUBA sources trace the same underlying population of high-redshift, dust-enshrouded galaxies. From a nearest-neighbour clustering analysis, we find tentative evidence that the most significant MAMBO sources come in pairs, typically separated by similar to23 arcsec. Our MAMBO observations unambiguously confirm around half of the SCUBA sources. In a robust subsample of 13 SMGs detected by both MAMBO and SCUBA at a significance greater than or equal to3.5sigma, only one has no radio counterpart. Furthermore, the distribution of 850 1200-mum flux density ratios for this subsample is consistent with the spectroscopic redshift distribution of radio-detected SMGs. Finally, we have searched for evidence of a high-redshift tail of SMGs amongst the 18 MAMBO sources that are not detected by SCUBA. Although we cannot rule out that some of them are SCUBA drop-outs at zmuch greater than3, their overall 850-to-1200 mum flux distribution is statistically indistinguishable from that of the 13 SMGS which were robustly identified by both MAMBO and SCUBA.