He woke up on their catamaran, a 47ft vessel called Siren Song, in the US Virgin Islands on Monday, but she was nowhere to be seen.
Ms Heslop’s belongings and passport were left on board, with her boyfriend telling the US Coast Guard he feared she might have fallen overboard.
He said: “She is loved by everyone who knows her. Sarm’s sense of adventure took her to the Caribbean, and like wherever she goes, she had made many friends.
“She is such a loving, fun girl. We just want her back safe and sound.”
Ms Heslop previously worked as a flight attendant and in call centres and is originally from Southampton.
Police have been searching the ocean in St John, but there has been no sign of her.
Toby Derima, Police Department Public Information Officer, said: “An English woman has gone missing on our island and we are appealing for help in trying to locate her.
“Unfortunately, this effort proved unsuccessful.
“She was last seen on Sunday aboard her boat which was moored off the coast of St. John.
“Every day that goes by and we don’t have any news about her is a major concern for us.
“We need to locate her as soon as possible.”
Ms Heslop is described as a white female of average built and height.
She has a southern English accent with a butterfly tattoo on her left shoulder.