Abstract The Cretaceous Chalk in England forms dual-porosity aquifers, with low-permeability matrix and high-permeability networks of fissures, which are predominantly stress-relief fractures that have been enlarged by dissolution. This enlargement is a function of the volume of water that has passed along a fracture (the flowrate effect) and its degree of chemical undersaturation. Feedback effects result in the development of a distinctive permeability structure, with four particular characteristics: (i) troughs in the water table with high transmissivity and convergent groundwater flow; (ii) substantial increases in transmissivities in a downgradient direction; (iii) downgradient decreases in hydraulic gradient; and (iv) discharge from the high-transmissivity zones to the surface commonly at substantial springs. This distinctive self-organized permeability structure occurs throughout unconfined chalk aquifers. Early enlargement of fissures at a depth of 50–100 m below the water table is slow, but is much more rapid close to the water table and in the uppermost bedrock due to non-linear dissolution kinetics. A modelled dissolution profile shows that more than 95% of dissolution takes place in the top 1 m of bedrock, and that enlargement of fissures in the saturated zone results from progressive dissolution occurring over a period of a million years or more.