  We present the spectroscopic analysis of a large sample of late-M, L, and T
dwarfs from UKIDSS. Using the YJHK photometry from ULAS and the red-optical
photometry from SDSS we selected a sample of 262 brown dwarf candidates and we
followed-up 196 of them using X-shooter on the VLT. The large wavelength
coverage (0.30-2.48 $\mu$m) and moderate resolution (R~5000-9000) of X-shooter
allowed us to identify peculiar objects including 22 blue L dwarfs, 2 blue T
dwarfs, and 2 low gravity M dwarfs. Using a spectral indices-based technique we
identified 27 unresolved binary candidates, for which we determined the
spectral type of the potential components via spectral deconvolution. The
spectra allowed us to measure the equivalent width of the prominent absorption
features and to compare them to atmospheric models. Cross-correlating the
spectra with a radial velocity standard, we measured the radial velocity for
our targets, and we determined the distribution of the sample, which is centred
at -1.7$\pm$1.2 km s$^{-1}$ with a dispersion of 31.5 km s$^{-1}$. Using our
results we estimated the space density of field brown dwarfs and compared it
with the results of numerical simulations. Depending on the binary fraction, we
found that there are (0.85$\pm$0.55) x 10$^{-3}$ to (1.00$\pm$0.64) x 10$^{-3}$
objects per cubic parsec in the L4-L6.5 range, (0.73$\pm$0.47) x 10$^{-3}$ to
(0.85$\pm$0.55) x 10$^{-3}$ objects per cubic parsec in the L7-T0.5 range, and
(0.74$\pm$0.48) x 10$^{-3}$ to (0.88$\pm$0.56) x 10$^{-3}$ objects per cubic
parsec in the T1-T4.5 range. There seem to be an excess of objects in the L/T
transition with respect to the late T dwarfs, a discrepancy that could be
explained assuming a higher binary fraction than expected for the L/T
transition, or that objects in the high-mass end and low-mass end of this
regime form in different environments, i.e. following different IMFs.
