  We present 2271 radial velocity measurements taken on 118 single-line binary
stars, taken over eight years with the CORALIE spectrograph. The binaries
consist of F/G/K primaries and M-dwarf secondaries. They were initially
discovered photometrically by the WASP planet survey, as their shallow eclipses
mimic a hot-Jupiter transit. The observations we present permit a precise
characterisation of the binary orbital elements and mass function. With
modelling of the primary star this mass function is converted to a mass of the
secondary star. In the future, this spectroscopic work will be combined with
precise photometric eclipses to draw an empirical mass/radius relation for the
bottom of the mass sequence. This has applications in both stellar astrophysics
and the growing number of exoplanet surveys around M-dwarfs. In particular, we
have discovered 34 systems with a secondary mass below $0.2 M_\odot$, and so we
will ultimately double the known number of very low-mass stars with well
characterised mass and radii.
  We are able to detect eccentricities as small as 0.001 and orbital periods to
sub-second precision. Our sample can revisit some earlier work on the tidal
evolution of close binaries, extending it to low mass ratios. We find some
binaries that are eccentric at orbital periods < 3 days, while our longest
circular orbit has a period of 10.4 days.
  By collating the EBLM binaries with published WASP planets and brown dwarfs,
we derive a mass spectrum with twice the resolution of previous work. We
compare the WASP/EBLM sample of tightly-bound orbits with work in the
literature on more distant companions up to 10 AU. We note that the brown dwarf
desert appears wider, as it carves into the planetary domain for our
short-period orbits. This would mean that a significantly reduced abundance of
planets begins at $\sim 3M_{\rm Jup}$, well before the Deuterium-burning limit.
[abridged]
