Britt Strandberg achieved major success in relay events. She was part of the Swedish relay team that won gold at the 1960 Winter Olympics at Squaw Valley, silver in the 1964 Olympic Winter Games at Innsbruck and silver in the 1968 Winter Olympics at Grenoble. She was the only skier who was a member of all three medal winning teams. With the Swedish relay team she also won silver at the World Cup in 1962 in Zakopane and bronze in the 1966 World Cup in Oslo. Individually, she won only one Swedish Championship – over the 10 km in 1961, but she won six relay titles including four consecutive victories from 1961 to 1966 and another two in 1966-67 with her club Edsbyns IF.