We have carried out a joint photometric and structural analysis of red sequence galaxies in four clusters at a mean redshift of ˜ 1.25 using optical and near-infrared Hubble Space Telescope imaging reaching to at least three magnitudes fainter than M*. As expected, the photometry and overall galaxy sizes imply purely passive evolution of stellar populations in red sequence cluster galaxies. However, the morphologies of red sequence cluster galaxies at these redshifts show significant differences to those of local counterparts. Apart from the most massive galaxies, the high-redshift red sequence galaxies are significantly discier than their low-redshift analogues. These galaxies also show significant colour gradients, again not present in their low-redshift equivalents, most straightforwardly explained by radial age gradients. A clear implication of these findings is that red sequence cluster galaxies originally arrive on the sequence as disc-dominated galaxies whose discs subsequently fade or evolve secularly to end up as high Sérsic index early-type galaxies (classical S0s or possibly ellipticals) at lower redshift. The apparent lack of growth seen in a comparison of high- and low-redshift red sequence galaxies implies that any evolution is internal and is unlikely to involve significant mergers. While significant star formation may have ended at high redshift, the cluster red sequence population continues to evolve (morphologically) for several gigayears thereafter.