A Lyttelton couple rescued from their yacht at a cost of nearly $1 million are being investigated by Work and Income.

Bruce Cox and Heloise Kortekaas, who revealed they were engaged after being snatched to safety from their disabled yacht last month, are understood to be under scrutiny for allegedly failing to reveal they were in a relationship while each was receiving a single person's benefit.

An investigator from Winz said Ms Kortekaas and Mr Cox were aware they were being investigated but Ms Kortekaas, 46, denied all knowledge of the inquiry.

"I don't know anything about that. I've never been on benefit for years." Mr Cox could not be contacted for comment.