It is a nice song.

The 'sweet Thames, flow softly' may come via T S Eliot from the Elizabethan poet Spenser. Apologies if somebody has pointed this out before.

CALM was the day, and through the trembling air
Sweet breathing Zephyrus did softly play,
A gentle spirit, that lightly did delay
Hot Titan's beams, which then did glister fair;
When I whose sullen care,
Through discontent of my long fruitless stay
In prince's court, and expectation vain
Of idle hopes, which still do fly away
Like empty shadows, did afflict my brain,
Walked forth to ease my pain
Along the shore of silver streaming Thames,
Whose rutty bank, the which his river hems,
Was painted all with variable flowers,
And all the meads adorned with dainty gems,
Fit to deck maidens' bowers,
And crown their paramours,
Against the bridal day, which is not long:
      Sweet Thames, run softly, till I end my song.

And Eliot alludes to this in his The Waste Land

The river's tent is broken: the last fingers of leaf
Clutch and sink into the wet bank. The wind
Crosses the brown land, unheard. The nymphs are departed.175
Sweet Thames, run softly, till I end my song.176
The river bears no empty bottles, sandwich papers,
Silk handkerchiefs, cardboard boxes, cigarette ends
Or other testimony of summer nights. The nymphs are departed.
And their friends, the loitering heirs of city directors;180
Departed, have left no addresses.
By the waters of Leman I sat down and wept...
Sweet Thames, run softly till I end my song,
Sweet Thames, run softly, for I speak not loud or long.
But at my back in a cold blast I hear185
The rattle of the bones, and chuckle spread from ear to ear.