In 2005, Murdoch went to his first ever World Championships. At the 2005 Ford World Men's Curling Championship his Scotland rink won the silver medal after losing to Canada's Randy Ferbey in the final. The team's fine run of form ensured all four members a place in the Great Britain men's squad for the 2006 Winter Olympics, with Murdoch in the position of skip. At the Olympics, Murdoch and his team lost in the bronze medal match to Pete Fenson of the United States. Two months later, Murdoch would avenge his defeat in 2005 by winning the gold medal at the 2006 World Men's Curling Championship. Murdoch defeated Canada (skipped by Jean-Michel Ménard) in the final. In December 2006 he won the silver medal in the European Championships in Basel, Switzerland, and followed that up with gold in 2007. He successfully defended his title at the European Curling Championships 2008 against Norway's Thomas Ulsrud.