From a sample of spectra of 439 white dwarfs (WDs) from the ESO-VLT Supernova-Ia Progenitor Survey (SPY), we measure the maximal changes in radial velocity ({Delta}RVmax) between epochs (generally two epochs, separated by up to 470d), and model the observed {Delta}RVmax statistics via Monte Carlo simulations, to constrain the population characteristics of double WDs (DWDs). The DWD fraction among WDs is f_bin_=0.10+/-0.02 (1{sigma}, random) +0.02 (systematic), in the separation range <~4au within which the data are sensitive to binarity. Assuming the distribution of binary separation, a, is a power law, dN/da{prop.to}a^alpha^, at the end of the last common-envelope phase and the start of solely gravitational-wave-driven binary evolution, the constraint by the data is alpha=-1.3+/-0.2(1{sigma}) +/-0.2 (systematic). If these parameters extend to small separations, the implied Galactic WD merger rate per unit stellar mass is R_merge_=(1-80)x10^-13^yr^-1^M_[sun}_^-1^ (2{sigma}), with a likelihood-weighted mean of R_merge_=(7+/-2)x10^-13^yr^-1^M_{sun}_^-1^ (1{sigma}). The Milky Way's specific Type Ia supernova (SN Ia) rate is likely R_Ia_~=1.1x10^-13^yr^-1^M_{sun}_^-1^ and therefore, in terms of rates, a possibly small fraction of all merging DWDs (e.g. those with massive-enough primary WDs) could suffice to produce most or all SNe Ia.