Models of the chemical evolution of our Galaxy are extended to include radial migration of stars and flow of gas through the disc. The models track the production of both iron and alpha elements. A model is chosen that provides an excellent fit to the metallicity distribution of stars in the Geneva-Copenhagen survey (GCS) of the solar neighbourhood, and a good fit to the local Hess diagram. The model provides a good fit to the distribution of GCS stars in the age-metallicity plane although this plane was not used in the fitting process. Although this model's star-formation rate is monotonic declining, its disc naturally splits into an alpha-enhanced thick disc and a normal thin disc. In particular the model's distribution of stars in the ([O/Fe],[Fe/H]) plane resembles that of Galactic stars in displaying a ridge line for each disc. The thin-disc's ridge line is entirely due to stellar migration and there is the characteristic variation of stellar angular momentum along it that has been noted by Haywood in survey data. Radial mixing of stellar populations with high sigma_z from inner regions of the disc to the solar neighbourhood provides a natural explanation of why measurements yield a steeper increase of sigma_z with age than predicted by theory. The metallicity gradient in the ISM is predicted to be steeper than in earlier models, but appears to be in good agreement with data for both our Galaxy and external galaxies. The models are inconsistent with a cutoff in the star-formation rate at low gas surface densities. The absolute magnitude of the disc is given as a function of time in several photometric bands, and radial colour profiles are plotted for representative times.

22 pages, 21 figures, 1 table updated to new GCS data release, slightly revised, accepted by MNRAS