Canada had medalled at every event since curling was introduced to the Olympics in 1998, twice taking gold, but after a tense 6-5 defeat to Britain where they made a series of mistakes, they have a record of three wins and five defeats with one match remaining and cannot progress to the semi-finals.
The result is a huge blow to Canada but was always a possibility after they started their campaign with three straight defeats and though they recovered well, a defeat to China on Tuesday piled on the pressure.
Britain, gold medallists in 2002 and who won bronze in 2014, played a superb and patient all-round game to take their tally to 6-3 and secure a last-four berth where they will face double gold medallists and Sochi runners-up Sweden after they beat China 8-4.
Already-qualified Korea underlined their credentials after thrashing the Olympic Athletes from Russia team 11-2 and will face either Japan or the United States following the final set of round-robin preliminaries later on Wednesday.
(Reporting by Mitch Phillips; editing by Sudipto Ganguly)