Welford's playing position was as a full-back, he had played for Stockton F.C. and Bishop Auckland F.C., before joining Birmingham St George's F.C., from where he joined Aston Villa F.C. in 1893. He played for Aston Villa from 1893 to 1896, making a total of 83 appearances in both League and Cup, scoring one goal. While at Villa, he formed a key partnership in defence with Bob Chatt. He won the 1895 FA Cup with Aston Villa. From Aston Villa he moved to Celtic in Scotland, where he played for three seasons and won the Scottish Football League in 1897–98 followed by the Scottish Cup in 1899.