Which star of 1986 said "It's not just old perverts who are my fans?"
Sheena Easton has been suggested but I am unable to confirm this.

My guess is Samantha Fox.  She was the face of Twingo Bingo for The
Sun, and she certainly might have said this statement due to her
appearances sans full clothing in publications such as The Sun. 
(Indeed, I won't like to the "Page 3" archive noting her ads for
Twingo Bingo, due to a lack of clothing above the waist.)