The United Kingdom is funding a program of astronomical adaptive optics (AO), the primary purpose of which is to equip two 4-meter telescopes with common-user (facility) natural guide star AO systems: the 4.2 m William Herschel Telescope on La Palma in the Canary Islands and the 3.8 m United Kingdom Infrared Telescope on Mauna Kea, Hawaii. The program also supports related developments in the following fields: site evaluation (on La Palma and Mauna Kea), IR instrumentation, adaptive secondary mirror design, partial AO, and laser beacons (for La Palma). The structure, purposes, and timescales of the overall program are described. In general, the goal is to deliver AO systems which have wide astronomical application and provide well-optimized performance in a wide range of environmental conditions. The ways in which this goal has conditioned the program are outlined.