We report the discovery of a very cool d/sdL7+T7.5p common proper motion binary system, SDSS J1416+13AB, found by cross-matching the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Large Area Survey Data Release 5 (UKIDSS LAS DR4) against the Sloan Digital Sky Survey Data Release 7. The d/sdL7 is blue in J - H and H - K and has other features suggestive of low metallicity and/or high gravity. The T7.5p displays spectral peculiarity seen before in earlier type dwarfs discovered in UKIDSS LAS DR4, and referred to as CH4-J-early peculiarity, where the CH4-J index, based on the absorption to the red side of the J-band peak, suggests an earlier spectral type than the H2O-J index, based on the blue side of the J-band peak, by ~2 subtypes. We suggest that CH4-J-early peculiarity arises from low metallicity and/or high gravity, and speculate as to its use for classifying T dwarfs. UKIDSS and follow-up United Kingdom Infrared Telescope/Wide Field CAMera (UKIRT/WFCAM) photometry shows the T dwarf to have the bluest near-infrared colours yet seen for such an object with H - K = -1.31 +/- 0.17. Warm Spitzer IRAC photometry shows the T dwarf to have extremely red H - [4.5] = 4.86 +/- 0.04, which is the reddest yet seen for a substellar object. The lack of parallax measurement for the pair limits our ability to estimate parameters for the system. However, applying a conservative distance estimate of 5-15 pc suggests a projected separation in range 45-135 au. By comparing H - K:H - [4.5] colours of the T dwarf to spectral models, we estimate that Teff = 500 K and [M/H] ~ - 0.30, with logg ~ 5.0. This suggests a mass of ~30 MJupiter for the T dwarf and an age of ~10 Gyr for the system. The primary would then be a 75 MJupiter object with logg ~ 5.5 and a relatively dust-free Teff ~ 1500K atmosphere. Given the unusual properties of the system we caution that these estimates are uncertain. We eagerly await parallax measurements and high-resolution imaging which will constrain the parameters further.