Jay Merriman-Mukoro, who worked as assistant producer on Andrew Marr's Bafta-winning History of Modern Britain, was on holiday with his wife when he went into the water at Accra Beach last Sunday.
A body has been recovered and DNA testing is being carried out to determine whether it is that of the 43-year-old, the BBC reported.
The documentary maker and his psychologist wife Olivia, who married last September, had travelled to the Caribbean island for a wedding.
While there he conducted an interview for a Commonwealth Games documentary for the BBC, in what was to be his directorial debut.
His colleagues at BBC Scotland, where he had recently been working on a freelance basis, described him as a "popular and respected friend and colleague".
Dr Merriman-Mukoro said that leaving Barbados to return home to London had been "very, very painful" but praised her husband's "great sense of energy and enthusiasm".
Speaking to the BBC, she said: "Pre-Barbados was a time when Jay and I were a very well-matched and happy couple, making plans for our future.
"Now, post-Barbados is a time when I will have to face a new life without him."
She explained that a yellow flag was in place to warn of choppy conditions when Mr Merriman-Mukoro went into the water, but it did not seem rougher than usual.
Looking up from reading her book she saw a man who appeared to be her husband but panicked when she realised it was not.
Lifeguards and the coastguard carried out the search, but it was only until days later that a body was found further along the coast.
Authorities in Barbados have said it could be several days before DNA tests are complete.
"In one way we don't want to give up this glimmer of hope that he could still be alive," Dr Merriman-Mukoro said.
"But there's something important about having closure so we can repatriate him and have a memorial service at home, to be able to mourn Jay in a more physical way."
In a statement to the BBC, Mr Merriman-Mukoro's family said they were "devastated".
"To think that Jay may no longer be in our lives is incomprehensible," they said.
"He's very humble, very gentle, very honourable, hard-working. He's the life and soul of the party.
"We as a family will have to try to make sense of what has happened and the enormity of what is before us."
A spokesman for the Foreign Office said: "We are aware that a British national has been reported missing in Barbados on April 20.
"We are providing consular assistance to the family at this difficult time."