We report the discovery of three very late T dwarfs in the UKIRT Infrared Deep Sky Survey (UKIDSS) Third Data Release: ULAS J101721.40+011817.9 (ULAS1017), ULAS J123828.51+095351.3 (ULAS1238) and ULAS J133553.45+113005.2 (ULAS1335). We detail optical and near-infrared (NIR) photometry for all three sources, and mid-IR photometry for ULAS1335. We use NIR spectra of each source to assign spectral types T8p (ULAS1017), T8.5 (ULAS1238) and T9 (ULAS1335) to these objects. ULAS1017 is classed as a peculiar T8 (T8p) due to appearing as a T8 dwarf in the J band, whilst exhibiting H- and K-band flux ratios consistent with a T6 classification. Through comparison to BT-Settl model spectra we estimate that ULAS1017 has 750K <~ Teff <~ 850K, and 5.0 <~ logg(cms-2) <~ 5.5, assuming solar metallicity. This estimate for gravity is degenerate with varying metallicity. We estimate that ULAS1017 has an age of 1.6-15 Gyr, a mass of 33-70MJ and lies at a distance of 31-54 pc. We do not estimate atmospheric parameters for ULAS1238 due to a lack of K-band photometry. We extend the unified scheme of Burgasser et al. to the type T9 and suggest the inclusion of the WJ index to replace the now saturated J-band indices. We propose ULAS1335 as the T9 spectral type standard. ULAS1335 is the same spectral type as ULAS J003402.77-005206.7 and CFBDS J005910.90-011401.3. We argue that given the similarity of the currently known >T8 dwarfs to the rest of the T dwarf sequence, the suggestion of the Y0 spectral class for these objects is premature. Comparison of model spectra with that of ULAS1335 suggest a temperature below 600 K, possibly combined with low gravity and/or high metallicity. We find ULAS1335 to be extremely red in NIR to mid-IR colours, with H - [4.49] = 4.34 +/- 0.04. This is the reddest NIR to mid-IR colour yet observed for a T dwarf. The NIR to mid-IR spectral energy distribution of ULAS1335 further supports Teff < 600 K, and we estimate Teff ~ 550-600K for ULAS1335. We estimate that ULAS1335 has an age of 0.6-5.3 Gyr, a mass of 15-31MJ and lies at a distance of 8-12 pc.