Dominic Bernard, 18, from Epsom, Surrey, travelled to the South American country in October but has made no contact since landing in Timehri.
A badly decomposed body was found in a shallow grave in the Berbice region last Friday, and relatives were told it was almost certainly Mr Bernard.
Post-mortem examinations found a fractured skull and broken neck
Police are reported to have recovered a hammer, thought to have been one of the murder weapons.
Guyana's police chief has told the BBC that he is applying to the courts for more time to hold the suspects pending further tests on the body.
The BBC's reporter in Guyana, Colin Smith, said he had also been told two of the suspects had made detailed confessions.
Mr Bernard's family said he had travelled in October to pursue his dream of studying film-making.
His parents Andrew and Linda said their son was "full of hope, ambition, creativity, self-respect, faith and trust".
They said he was "chasing his dreams, exploring his heritage and doing the things that brought joy to his heart".
Surrey Police said authorities in Guyana had notified them that a body had been found in the search for Mr Bernard.
"Although the body has yet to be formally identified, Surrey Police officers, including specialist family liaison officers, are providing the Bernard family with updates and support at this difficult time," it said in a statement.
The investigation was being led by the Guyana Police Force, it added, but Surrey Police would "continue to liaise with all relevant agencies as inquiries continue".
Seven people have been arrested on suspicion of murdering of an aspiring British film-maker in Guyana.