Contractors moved on site last week to start taking down the building, which has been a feature of the Chesterfield townscape for decades.
Chesterfield Borough Council was granted planning permission to open a temporary car park with a total of 88 spaces at the Malkin Street location.
The proposals will see the existing Chesterfield Hotel car park returned to use alongside a temporary open surface car park, which is to be built on the footprint of the old hotel.