We present the discovery of fifteen new T2.5-T7.5 dwarfs (with estimated distances between 24–93pc), identified in the first three main data releases of the UKIRT Infrared Deep Sky Survey. This brings the total number of T dwarfs discovered in the Large Area Survey (to date) to 28. These discoveries are confirmed by near infrared spectroscopy, from which we derive spectral types on the unified scheme of Burgasser et al. (2006). Seven of the new T dwarfs have spectral types of T2.5-T4.5, five have spectral types of T5-T5.5, one is a T6.5p, and two are T7-7.5. We assess spectral morphology and colours to identify T dwarfs in our sample that may have non-typical physical properties (by comparison to solar neighbourhood populations), and find that one of these new T dwarfs may be metal poor, three may have low surface gravity, and one may have high surface gravity. The colours of the full sample of LAS T dwarfs show a possible trend to bluer Y −J with decreasing effective temperature, and some interesting colour changes in J −H and z−J (deserving further investigation) beyond T8. The LAS T dwarf sample from the first and second main data releases show good evidence for a consistent level of completion to J=19. By accounting for the main sources of incompleteness (selection, follow-up and spatial) as well as the effects of unresolved binarity and Malmquist bias, we estimate that there are 17±4 >T4 dwarfs in the J 619 volume of the LAS second data release. Comparing this to theoretical predictions is most consistent with a sub-stellar mass function exponent α between -1.0 and 0. This is consistent with the latest 2MASS/SDSS constraint (which is based on lower number statistics), and is significantly lower than the α 1.0 suggested by L dwarf field populations, possibly a result of the lower mass range probed by the T dwarf class.