HONG KONG—A former employee of Britain’s Hong Kong consulate claimed Chinese secret police beat him, deprived him of sleep and chained him spread-eagled as they pressed him for information about activists leading the pro-democracy protests that have swept the city since June.

In a series of interviews, Simon Cheng, a Hong Kong citizen who worked for the U.K. mission’s business-development team when he was detained, told The Wall Street Journal he also was questioned repeatedly about the role his interrogators presumed Britain...