"Unreal City   
  Under the brown fog of a winter noon  
  Mr. Eugenides, the Smyrna merchant  
  Unshaven, with a pocket full of currants
  C..i.f. London: documents at sight,  
  Asked me in demotic French  
  To luncheon at the Cannon Street Hotel  
  Followed by a weekend at the Metropole."
"This music crept by me upon the waters"
 [And along the Strand, and up the ghastly hill of Cannon Street,
  Fading at last, behind my flying feet]
One might explain the "flying feet" here in two ways:
1. A person, especially one endowed with a puritanical and metaphysical sensibility ("Unreal City"), would run away from something that that person considered evil -- in this case, the "ghastly" hill of Cannon Street.
2. Generally, a walk up the hill is arduous and slow, a walk down perforce fast and brisk. 
Put simply, the widely pervasive sensual music ["this music"] kept resonating in the narrator's ears through his long-winded excursion through the waste land [here of London] -- receding, finally, only after he got fast farther from the "ghastly" hill.
Since Euginedes, the Smyrna merchant, had shown the audacity [in the narrator's eyes] to invite him, a person of puritanical sensibility,  to places notorious as homosexual haunts, the narrator would be doubly wary passing through, what appeared to him, a place of evil and sin. The sensual music
("This music") around the "ghastly" hill would, of course, resound as dissolute to his puritanical ears as the depraved tumult of Carthage to Augustine's ears.
"This music crept by me upon the waters"
And along the Strand, up Queen Victoria Street...
Down Greenwich reach
Past the Isle of Dogs.
Weialala leia
Wallala leialala"
"la la
 To Carthage then I came"
[Eliot's Note: St. Augustine's Confessions: "to Carthage then I came, where a cauldron of unholy loves sang all about mine ears."]