I'm afraid Labric is slightly overdoing it: at night, the Hinckley chimes sounded every three hours (not every 15 minutes).
Moreover, they did not produce a descending scale, but a tune: actually, there were seven tunes "programmed" into the mechanism, one for each day of the week, and Vierne must have drawn the main theme of his composition from the tune that sounded on the particular night he was staying there.
A much more likely source of inspiration for the descending scales (of which Vierne did indeed put 28(!) in a row at the end of his composition) would be
change ringing: it is very likely that Vierne had the opportunity to listen to some of it during his stay in Britain (possibly in Hinckley itself).