LONDON — The founder and chief executive of the British fashion chain Ted Baker resigned on Monday after current and former employees accused him of inappropriate behavior. Employees said the executive, Ray Kelvin, would regularly try to massage people in the office, insist on long hugs with staff members, and ask employees for sex, according to a petition that started circulating in December. The petition also said that the company’s human resources department had ignored complaints about the behavior. “Harassment at Ted Baker is well documented but willfully ignored by those in charge,” wrote the authors of the petition, which called for the company to adopt procedures that would allow workers to report harassment to an independent, external organization. Mr. Kelvin denied the allegations, but agreed on Monday to resign immediately as chief executive and director of Ted Baker, the company said.