Concerning the passages spoken by the three Thames-daughters, Eliot's note to line 266 directs us to Götterdämmerung, the last of the four operas of Der Ring des Nibelungen Ring cycle. Specifically Eliot directs us to act 3, scene 1, available here (but in German only.) There Wagner's three Rhine-daughters sing two refrains of "Weialala leia, wallala leialala" and one of "la la" to the hero of the Ring cycle, Siegfried.
To fully understand this allusion one must go the first of Wagner's Ring operas, Das Rheingold. A small portion of Das Rheingold is available here, (but in German only.) In The Rhinegold Eliot's song is not an exact match of Wagner's but in the first act of the opera there are numerous occurances in many places of a Wallala sound. All appear in the first scene, the one with the Rhine-daughters and Alberich, the thief of the Rhinegold. They are:
Additionally, the scene in The Rhinegold ends with the Rhine-daughters singing a lament of "Weh! Weh!, (roughly translated as "Woe, Woe.") Perhaps one should think of this when the "la la" of line 306 is encountered.
Wallala, weiala weia!
Wallala! Lalaleia! Leialalei!
Wallala! Lalaleia! Leialalei!
Heiajaheia! Wallalalalala leiajahei!
Wallalalala leialalai! Wallalalala leiajahei!
Heiajaheia! Heiajaheia! Wallalalala leiajahei!
Eliot may be referring us to Götterdämmerung instead of Das Rheingold because of the fire imagery in Götterdämmerung. Brünnhilde rides her horse into Siegfried's funeral pyre and Valhalla, the abode of the gods, is destroyed by flame.
Here is a description of the first scene of Das Rheingold (from the web site of the Arizona Opera):
The curtain rises over the Rhine River, in which the Rhinemaidens, sister creatures to mermaids of the sea, gradually gather to share their girlish games and songs. Their lighthearted playfulness belies the solemn nature of their primary responsibility: that of guarding the Rhine gold.
The Maidens' joyous singing soon attracts the attention of a hideous gnome, Alberich, whom they tease and tantalize, and generally make sport of until he reacts in angered frustration.
A shaft of light from the Heavens suddenly illuminates the Rhine treasure, the priceless hoard of gold they've been instructed to oversee. In their own gossipy fashion, the Maidens explain to Alberich the curse faced by any potential thieves. The gold may be forged into a Ring which will allow its owner to rule the World, however, its possessor must forswear love forever and live in emotional desolation.
After his humiliating experience with the Rhinemaidens, Alberich is convinced he has no need of feminine affection - now or ever. He curses love, plunges into the Rhine, wrenches the treasure from its hiding place, and disappears as the terrified Maidens helplessly attempt to detain him. Once the gold disappears, all grows dark.
Here is a description of the first scene of the third act of Götterdämmerung (from the Walhall (Valhalla) web site - http://walhall.com/syngott.html) The action takes place in a forest on the bank of the Rhine River.
The Rhine maidens call for the champion who will return their gold. Siegfried, having lost track of the bear he was hunting, comes upon them, and they ask for the Ring in return for pointing him aright. When he protests that his wife would scold him for making such a poor bargain, they tease him about being henpecked, then warn him of the evil consequences should he keep the Ring. Siegfried replies that he could have been cajoled out of the Ring by such lusty maidens, but he will turn a deaf ear to their warnings.