Foreign foundations for Type 31 and Constellation

Do the Royal Navy or US Navy ever buy warship designs from other countries?

Yes; Type 31 and the Constellation-class frigate both use foreign design foundations.

The Royal Navy and US Navy have bought foreign warship designs, although both more often sell designs to other countries. Type 31 is the recent British example. The Constellation-class frigate is the American example. Both demonstrate that a navy with its own design industry can still purchase a foreign basis for a ship.