Liquid crystal 'blue phases' are highly fluid self-assembled three-dimensional cubic defect structures that exist over narrow temperature ranges in highly chiral liquid crystals. The characteristic period of these defects is of the order of the wavelength of visible light, and they give rise to vivid specular reflections that are controllable with external fields. Blue phases may be considered as examples of tuneable photonic crystals with many potential applications. The disadvantage of these materials, as predicted theoretically and proved experimentally, is that they have limited thermal stability: they exist over a small temperature range (0.5-2 degrees C) between isotropic and chiral nematic (N*) thermotropic phases, which limits their practical applicability. Here we report a generic family of liquid crystals that demonstrate an unusually broad body-centred cubic phase (BP I*) from 60 degrees C down to 16 degrees C. We prove this with optical texture analysis, selective reflection spectroscopy, Kössel diagrams and differential scanning calorimetry, and show, using a simple polarizer-free electro-optic cell, that the reflected colour is switched reversibly in applied electric fields over a wide colour range in typically 10 ms. We propose that the unusual behaviour of these blue phase materials is due to their dimeric molecular structure and their very high flexoelectric coefficients. This in turn sets out new theoretical challenges and potentially opens up new photonic applications.