We present the second paper of a series of publications aiming at obtaining a better understanding regarding the nature of type Ia supernovae (SN Ia) progenitors by studying a large sample of detached F, G and K main-sequence stars in close orbits with white dwarf companions (i.e. WD+FGK binaries). We employ the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) data release 4 spectroscopic data base together with Galaxy Evolution Explorer (GALEX) ultraviolet fluxes to identify 1549 WD+FGK binary candidates (1057 of which are new), thus doubling the number of known sources. We measure the radial velocities of 1453 of these binaries from the available LAMOST spectra and/or from spectra obtained by us at a wide variety of different telescopes around the globe. The analysis of the radial velocity data allows us to identify 24 systems displaying more than 3{sigma} radial velocity variation that we classify as close binaries. We also discuss the fraction of close binaries among WD+FGK systems, which we find to be ~10 per cent, and demonstrate that high-resolution spectroscopy is required to efficiently identify double-degenerate SN Ia progenitor candidates.