  We present a new sample of mid L to mid T dwarfs with effective temperatures
of 1100 to 1700K selected from the UKIDSS Large Area Survey and confirmed with
infrared spectra from X-Shooter/VLT. This effective temperature range is
especially sensitive to the formation history of Galactic brown dwarfs and
allows us to constrain the form of the sub-stellar birth rate, with sensitivity
to differentiate between a flat (stellar like) birth rate, and an exponentially
declining form. We present the discovery of 63 new L and T dwarfs from the
UKIDSS LAS DR7, including the identification of 12 likely unresolved binaries,
which form the first complete sub-set from our program, covering 495 sq degrees
of sky, complete to J=18.1. We compare our results for this sub-sample with
simulations of differing birth rates for objects of mass 0.10-0.03Msol and ages
1-10Gyrs. We find that the more extreme birth rates (e.g. a halo type form) can
likely be excluded as the true form of the birth rate. In addition we find that
although there is substantial scatter we find a preference for a mass function,
with a power-law index, alpha in the range -1 < alpha < 0 that is consistent
(within the errors) with the studies of late T dwarfs.
