The scheme will see Chipperfield replace the G B Hart building from 1876 with a new 97-unit hotel backed by current owner The Thistle Group.
Adam Wilkinson of SAVE Britain's Heritage said: 'It's a very great pity that this building will be demolished. I'm quite confused really as it sits within a conservation area, so it asks what the point is in having conservation areas in the first place?'
According to a council spokesman, planning officers were satisfied with the 'substantial amendments' made by Chipperfield, and the scheme was rubber-stamped.
The north London-based practice was forced to resubmit its plans in December after the first proposals were thrown out. The new scheme now sees much of the existing building's facade retained.
Last night's planning meeting lasted nearly three hours, and the firm said it was 'delighted' by the decision.