The Lighthouse

From Muppet Wiki

The Lighthouse was the home of the Captain and Sprocket and the central framing location on the UK version of Fraggle Rock. In contrast to Doc's Workshop, the lighthouse was isolated on an island. Thus, the Captain received Uncle Traveling Matt's postcards from the passing mailboat and communicated with any friends or acquaintances, such as Commander Ponsonby, solely through mail and telephone. The lighthouse interior was relatively similar to Doc's workshop, however, one key addition was a chess set.

In the UK version of "Let the Water Run," the Captain refers to himself on the telephone as "Fraggle Rock Lighthouse Captain" implying that the name of the island on which the lighthouse is situated is in fact called "Fraggle Rock."

The exterior shots were of St. Anthony's Head Lighthouse at Falmouth Harbour in Cornwall, England.