The former ABC cinema in the centre of Tunbridge Wells has been derelict for nearly 14 years despite a number of demolition and redevelopment plans.
Work was due to start on Monday but work to make safe the electricity and gas supplies has delayed demolition.
A former dental surgery on the site will pulled down first, with the project due to take 12 weeks.
Liberal Democrat councillor Ben Chapelard, who has campaigned for the redevelopment of the site, has previously called it the town's "number one grot spot".
In February, the Conservative-led borough council issued a demolition notice on the owners.
Demolition of a derelict town centre cinema in Kent, branded as a "grot spot" is due to start this week.