We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα emission in a sample of eight gravitationally lensed galaxies at z = 1–1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from ∼10× to ∼50×. This enables us to identify resolved star-forming H ii regions at this epoch and therefore study their Hα luminosity distributions for comparisons with equivalent samples at z ∼ 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of H ii regions with redshift. The distribution of clump properties can be quantified with an H ii region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that ‘clumpy’ galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their H ii regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc.