The burnt body of Oliver Gobat from Esher was found in a car on the Caribbean island in April 2014.
After a campaign by his parents, the Home Secretary agreed UK police could assist investigators in St Lucia.
Surrey Police said no Surrey officer had travelled to St Lucia but they had been liaising with investigators there.
Speaking to BBC Surrey, Oliver Gobat's mother Helen said there were "people of interest" to interview in England.
"Seeking justice for him has been impossible - Ollie deserves a proper police investigation," she said.
"We are desperately frustrated. It is a solvable crime."
In September 2015 Surrey Police were given permission by Theresa May to help with the investigation.
A Surrey Police spokeswoman said: "Although no Surrey officer has travelled to the Caribbean island, St Lucian Police have been liaising with Surrey Police as part of their on-going investigation.
"As a matter of long-standing policy and practice, we neither confirm nor deny the existence of any mutual legal assistance requests."
Oliver, known as Ollie, was born in St Lucia but grew up in Surrey where he played junior cricket at county level.
He and his two older brothers ran a five-star boutique hotel in an exclusive resort in St Lucia.
The mother of a hotel owner shot dead in St Lucia has accused Surrey Police of "dragging their heels" over the murder investigation.