Demolition specialists Hughes and Salvidge started work to take down the concrete carbuncle two weeks ago, in a move which is hoped will kick-start redevelopment of the site.
The car park is now being dismantled following asbestos checks.
Worthing Borough Council, backed by government funding, agreed to seek demolition of the 1960s car park in September.
The council leases the car park from site owners Mosaic but it required an investment of £2million over the next four years.
As well as saving money, the council hopes the demolition will provide fresh impetus to Mosaic to redevelop the wider site.
It will open a temporary 66-space surface car park when the multi-storey is gone.
Mosaic has now notified the council of its intention to knock down the rest of the buildings on site - with the exception of Teville Gate House, which it does not own.