In the second branch of the Mabinogion, King Bendigeidfran and his men travel from Britain ("the Island of the Mighty", or Ynys Y Kedeirn), intent on avenging the punishment of his sister, Branwen, at the hands of the Irish (which takes place against the will of the Irish king Matholwch).
It is written that
Bendigeidfran, and the aforementioned hosting sailed towards Ireland. The ocean was not extensive [back] then: he went by wading. There used to be nothing except two rivers called the Lli and the Archen. And after that the ocean spread out, and the sea flooded the kingdoms. Then he advanced, carrying all the string-minstrels on his back, making for the land of Ireland.
Bendigeidfran was a giant, and so it was easy for him to cross, though the rivers were too deep for normal men to cross (he looks like a mountain from afar).
Why did the Lli and Archen rivers flood, creating an ocean (which we today call the Irish Sea)? The two are never mentioned again in the Mabinogion (I checked the three other branches), and Bendigeidfran soon drops out of the story (I won't spoil the reason why), so giants crossing rivers are not involved.
As a side note, the rivers seem purely fictional; I do not know if they show up in any other legends, though.