Brainteaser 1782: Unwinding

From The Sunday Times, 10th November 1996 [link]

Our Vienna clock will run for about eight days when fully wound, so I wind it up each Sunday morning. But last Sunday this caused a problem as, after I had wound it up, the hands started rotating at many times their normal speed. Thereafter they slowed down at a steady rate until they stopped sometime after 5pm.

Interestingly, they told the correct time on the hour at each hour between winding up and stopping.

What was the correct time when the clock stopped?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book.