Just looked at the lyrics in "The Essential Ewan MacColl Songbook," compiled by Peggy Seeger, 2001, pp. 30-31 (copyright 1968, Ewan MacColl Ltd.). The same as those posted by Leadfingers.
The title comes from Edmund Spencer, "Prothalamion":
Against their bridal day which is not long,
Sweet Thames, run softly, till I end my song.

Chords in the MacColl Songbook in part a little different from those given by Reiver 2. They were added to the MacColl songs by Peggy Seeger.

"Smoothly, not too fast"
I (D)met my girl at (A7)Wool-wich Pier,
Be-(D)neath a (G)big crane (A7)stand-ing,
And (D)O, the love I (A7)felt for her
It (D)passed all (A7)un-der-(D)stand-ing.
Took her sail-ing (Em)on the riv-er,
(G)Flow, sweet (A7)riv-er, flow,
(D)Lon-don town was (EM)mine to give her,
(G)Sweet (A7)Thames, flow (D)soft-ly.
(A7)Make the Thames in-to a crown,
(G)Flow, (D)sweet (A7)riv-er, flow,
(D)Made a brooch of (Em)Sil-ver-(A7)town,
(G)Sweet (D)Thames, flow (A7) soft- (D)ly.