OK, so it's not strictly part of the Dyfi Valley now, but how else could the Dyfi have met the sea in ancient times, other than by flowing through the now lost land of Cantre'r Gwaelod? So I feel entirely justified in including it here - and anyway, it's such a good yarn.

According to the official definition   http://www.jncc.gov.uk/protectedsites/SACselection/sac.asp?EUcode=UK0013117  "The Sarnau (Sarn Badrig, Sarn-y-Bwch and the Cynfelyn Patches [also called Sarn Cynfelyn]) are very unusual shallow subtidal reefs, which extend many kilometres into Cardigan Bay from the coast. They are glacial moraines resulting from the last glaciation and are composed entirely of boulders, cobbles and pebbles mixed with various grades of sediments."

Elsewhere I've found reference to 5 Sarnau:

Sarn Badrig, 21 miles long, extending from Mochras Island.
Sarn y Bwch, 1 mile long, located between Aberdyfi and Barmouth. (This is the correct name, and "Sarn y Bwlch" - quoted elsewhere - is erroneous. I've found many other examples of mutation in the names of geographical features which creep in through long oral use, lack of understanding of the original Welsh words, and even typos introduced by the Ordnance Survey - and these names then carry forward into posterity.)
Sarn Cynfelyn, 7-8 miles long, located 2 miles North of Aberystwyth. |Old Chart|
Sarn Dewi, quarter mile long. near Llandewi-Aberarth.
Sarn Cadwgan, 1 and 1/4 miles long, to the South of Sarn Dewi.

See map.

At very low tides you can clearly make out parts of these Sarnau, and I have clear childhood memories of low tides exposing the stumps of a petrified forest offshore at Borth. See http://www.bbc.co.uk/wales/mid/sites/borth/pages/submerged_forest.shtml

So, it's much more likely, isn't it, that the real story is that they are the remains of the dykes which surrounded a now-submerged kingdom of Cantre'r Gwaelod (The Bottom or Lowland Hundred). A convenient scapegoat named Seithenyn was supposed to have been looking after the flood gates when he (with much embellishment by those who love weaving stories) somehow failed miserably in his duties - I think alcohol was involved - and let the waters in, thereby flooding Cantre'r Gwaelod forever.

Well, that's one version: another authoritative sounding version: http://www.britannia.com/bios/ebk/gwyddgmd.html  tells that Seithenyn was a local king, and it was entirely his fault that a fair maiden called Mererid left the flood gates open. It's probably best not to question why poor Mererid was distracted by Seithenyn just at the wrong moment.

Whatever the case, it is still said that if you listen closely you can hear the bells of the lost city ringing out from under the sea.

Following the unfortunate inundation, Gwyddno Garanhir (Longshanks), King of Ceredigion (b. circa 490 AD) and brother of Maelgwn Gwynedd, relocated his court in something of a hurry to dry land, where his main port was established at Porth Wyddno (Borth) and where nearby he had a fishing weir constructed "between Aberdyfi and Aberystwyth", named Gored Wyddno. It was on this weir that Taliesin was discovered in a leather bag by the son of Gwyddno, Prince Elphin.

The Cantre'r Gwaelod story persisted for centuries, and as late as 1770 it was reported that there were remains of human habitation at the far end of Sarn Cynfelyn, "at a place called Caer Wyddno". William Owen Pughe wrote that "three or four miles in the sea between the outlets of the rivers Ystwyth and Teivi ... in the summer of 1770 I sailed over the ruins, on a very calm day and thus for about three minutes I had a clear view of them". In 1833, Samuel Lewis recorded in his Topographical Dictionary of Wales: "another of the features of Cardigan Bay, which could be seen at particularly low tides. Caer-Wyddno - the fort, or palace, of Gwyddno - is a collection of large stones and boulders, seven miles out to sea, west of Aberystwyth".