We present the discovery of fifteen new T2.5-T7.5 dwarfs ( with estimated distances between \sim 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 \pm 4 \geq T4 dwarfs in the J \leq 19 volume of the LAS second data release . Comparing this to theoretical predictions is most consistent with a sub-stellar mass function exponent \alpha 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 \alpha \sim 1.0 suggested by L dwarf field populations , possibly a result of the lower mass range probed by the T dwarf class .