Close double degenerate binaries are one of the favoured progenitor channels for type Ia supernovae, but it is unclear how many suitable systems there are in the Galaxy. We report results of a large radial velocity survey for double degenerate (DD) binaries using the UVES spectrograph at the ESO VLT (ESO SN Ia Progenitor surveY - SPY). Exposures taken at different epochs are checked for radial velocity shifts indicating close binary systems. We observed 689 targets classified as DA (displaying hydrogen-rich atmospheres), of which 46 turned out to possess a cool companion. We measured radial velocities (RV) of the remaining 643 DA white dwarfs. We managed to secure observations at two or more epochs for 625 targets, supplemented by eleven objects meeting our selection criteria from literature. The data reduction and analysis methods applied to the survey data are described in detail. The sample contains 39 double degenerate binaries, only four of which were previously known. 20 are double-lined systems, in which features from both components are visible, the other 19 are single-lined binaries. We provide absolute RVs transformed to the heliocentric system suitable for kinematic studies. Our sample is large enough to sub-divide by mass: 16 out of 44 low mass targets (0.45 Msun are double. Although the detected fraction amongst the low mass objects (36.4 +/- 7.3%) is significantly higher than for the higher-mass, carbon/oxygen-core dominated part of the sample (3.9 +/- 0.8%), it is lower than the detection efficiency based upon companion star masses >= 0.05 Msun. This suggests either companion stars of mass <0.05 Msun, or that some of the low mass white dwarfs are single.