The answer is the Shiants (pronounced "Shants"), a group of three small rocky islands in the Minch between the north west coast of Scotland and the island of Lewis in the Outer Hebrides. They're 20 miles from Rudha Reidh Lighthouse - the nearest point on the mainland - and 4 miles from the Uisenis Lighthouse, the nearest point on Lewis.
The picture below (courtesy of Traigh Mhor) shows the islands viewed from near Gairloch on the mainland. The photo is taken with a zoom lens making them look much closer than they actually are - they're about 30 miles from where the photographer is standing. Lewis and Harris are beyond.
The two main islands - Eilean an Taighe ("House Island") and Garbh Eilean ("Rugged Island") - are joined by a boulder strand called Mol Mor (Gaelic for "big shingle beach") which occasionally covers at its north end at exceptionally high spring tides but for most of the time it's possible to walk dry-shod between the two islands. The third island - Eilean Mhuire ("Mary's Island") - lies about half a mile to the east. In addition to these three, there is a string of jagged skerries to the west called the Galteachan.
The Shiants have not been permanently inhabited for about 200 years and today there is only one house, just a bothy really, at the north west end of Eilean an Taighe. It's only occupied for a few weeks in summer when the grazing tenant comes over from Lewis to tend to the flock of sheep on the islands. The picture below is of the shepherd (left) and my late father (right) at the door of the bothy in the mid 1980s on one of my several visits to the Shiants in the 70s and 80s.
And this is the bothy from up on the slopes of Eilean an Taighe:-
In the picture above you can see the remains of earlier dwellings in front of the cottage and the Ordnance Survey 6 inch map surveyed in 1852 shows a number of ruined buildings in this area - including a grave yard - although no sign of a permanent population.
The watercolourist, William Daniell, who made a tour of the west coast of Scotland around about 1820, called at the Shiants and made two paintings. He exaggerates the vertical extent of the islands but nevertheless captures their essence very well:-
The picture above is looking east along the north coast of Garbh Eilean.
That picture is looking west along the north coast of Garbh Eilean and an interesting detail in both of these pictures is the smoke from burning kelp - seaweed - which used to be gathered and burnt all along the west coast of Scotland to produce chemicals. It was a boom industry around the turn of the 19th century and Daniell's pictures are a valuable historical record of how the industry was prosecuted even in such a remote location.
One thing Daniell's watercolours do not exaggerate is the number of birds. The Shiants are an important breeding ground for a number of species including guillemots, razorbills, puffins, fulmars and kittiwakes. The numbers are overwhelming and I well recall the deafening (verging on sinister) sounds of the birds at night the first time I went to the Shiants in the mid 1970s on my father's Westerly Centaur 26 foot yacht and moored overnight in calm summer weather. The name Shiant is thought to derive from the Gaelic word sianta which has a range of meanings around "spooky", "haunted", "eerie" etc.
Above is a painting looking south from Garbh Eilean across the strand to the bothy on Eilean an Taighe which appeared on the cover of Scottish Field magazine in 1954 (image uploaded to Flickr by mando maniac). It employs some artistic licence (like William Daniell) but was clearly painted by someone who knew the islands.
The Shiants now belong to Adam Nicolson, a writer. His father, Nigel (son of Vita Sackville-West and Harold Nicolson, the founders of Sissinghurst Castle Gardens in Kent) bought them from Compton MacKenzie, author of Whisky Galore and Monarch of the Glen (on which the BBC series is loosely based), in 1937. Adam wrote a very good book about the islands in 2001 called Sea Room (which I read in Madeira - another fine archipelago!). There's also a very good website called shiantisles.net.
I leave you with a few more pictures from my visits to the islands in the 1980s. First, looking north along the west coast of Eilean an Taighe with the bothy towards Garbh Eilean:-
Looking over to Eilean Mhuire from the top of Eilean an Taighe:-
Next, looking over to Eilean Mhuire - the boat drawn up on the strand belonged to the shepherds who were there at the time:-
Looking from Eilean an Taighe along the east coast of Garbh Eilean to the natural arch at Toll a' Roimh at the island's north east corner:-
And finally, looking from Eilean an Taighe north west to the strand and Garbh Eilean. The Galteachan skerries and Lewis and Harris are visible beyond and, of course, our yacht (a Moody 29 by now) at anchor.