The excess numbers of blue galaxies at faint magnitudes are a long-standing cosmological puzzle. We present new number–magnitude counts as a function of galactic morphology from the first deep fields of the Cycle 4 Hubble Space Telescope Medium Deep Survey project. From a sample of 301 galaxies we define counts for elliptical, spiral and irregular/peculiar galaxies to I = 22. We find two principal results. First, the elliptical and spiral galaxy counts both follow the predictions of high-normalisation no-evolution models at all magnitudes, indicating that regular Hubble types evolve only slowly to z ~ 0.5. Secondly we find that irregular/peculiar galaxies, including multiple-peaked, possibly merging objects, have a very steep number–magnitude relation and greatly exceed predictions based on proportions in local surveys. These systems make up half the total counts by I = 22 and imply that the rapidly evolving component of the faint galaxy population has been identified.