Back when they had proper sports at the Olympics. Britain won the silver medal in the Tug of War, though as you can see it was a closely contested affair. The achievement was somewhat compromised by the fact that only Sweden and Great Britain entered.
Tug of war was contested as a team event in the Summer Olympics at every Olympiad from 1900 to 1920. Originally the competition was entered by clubs, which meant that one country could win several medals. This happened in 1904, when the United States won all three medals, and in 1908 when the podium was occupied by three British teams. Sweden was also among the top countries with two medals, one as a member of the mixed team.
The three winning British teams in 1908 were the City of London Police, Liverpool Police, and Metropolitan Police K Division: truly the golden age of law enforcement.