Ramsden was a left-back who made his debut for the club as a 19-year-old at Chelsea on the opening day of the 1937/38 season. Ramsden made 14 first division appearances during his debut season and also played in the fourth round FA Cup replay victory over Sheffield United in January 1938. He was only selected for ten League matches the following year but by the time the 1939/40 season opened he had become first-choice. Unfortunately, that season was suspended after only three games due to the outbreak of war.
Ramsden was 27 when the war ended and still considered as the club's first-choice left-back in August 1946. Although he lost his place after making 18 consecutive appearances from the start of the season, that was enough to qualify for a League Championship medal. At the end of the 1946/47 season it was reported that Ramsden was going to marry an American girl by the name of Audrey Clark and settle in New York where he was going to open a florist's business. He had met the girl when he saved the life of one of her relatives and was told to call on them when he was near New York and by fate Liverpool toured America in 1946. They fell in love and the rest should be history. Whatever happened between them the fact was that Ramsden returned for the 1947/48 season where he had to settle for playing second fiddle to Ray Lambert who took over his position.
Ramsden moved on to Sunderland in March 1948 before finishing his playing career with their North-East neighbours Hartlepools United. Ramsden was "a bit of a vocalist" and had an offer to perform in music halls, but he preferred to stay in football.