Brent Elsey says his nephew, Garrett Elsey of Sherwood Park, Alta., had only been in the UK a few hours when police in Bristol found his body on Thursday morning.
A BBC report says police are still working to establish the circumstances surrounding the death, and that officers searched stops where trucks collected bins for the facility.
Elsey, 22, had recently completed a bachelor's degree in history and political science from Ottawa's Carleton University.
His uncle says Elsey was to begin a master's degree in international security in Bristol.
"It's been very, very devastating. It's a very extensive family," Brent Elsey said on Saturday.
"We all thought he was going to turn into something very special."
Brent Elsey says police in the UK contacted the RCMP, who contacted the family.
Elsey says the unexplained circumstances of his nephew's death have also been making it hard on the family.
The BBC that police had searched up to eight different locations in Bristol in connection with the discovery of the body, but had later narrowed it down to one location.