K dwarfs have lifetimes older than the present age of the Galactic disc, and are thus ideal stars for investigating the chemical evolution of the disc. We have developed several photometric metallicity indicators for K dwarfs, based on a sample of accurate spectroscopic metallicities for 34 disc and halo G and K dwarfs. The photometric metallicities lead us to develop a metallicity index for K dwarfs based only on their position in the colour-absolute-magnitude diagram. Metallicities have been determined for 431 single K dwarfs drawn from the Hipparcos catalogue, selecting the stars by absolute magnitude and removing multiple systems. The sample is essentially a complete reckoning of the metal content in nearby K dwarfs. We use stellar isochrones to mark the stars by mass, and select a subset of 220 of the stars, which is complete within a narrow mass interval. We fit the data with a model of the chemical evolution of the solar cylinder. We find that only a modest cosmic scatter is required to fit our age-metallicity relation. The model assumes two main infall episodes for the formation of the halo-thick disc and thin disc, respectively. The new data confirm that the solar neighbourhood formed on a long time-scale of the order of 7Gyr.