Welford was born in Barnard Castle, County Durham; his playing position was as a full-back.

[1] While at Villa (where his teammates included Bob Chatt, also from Barnard Castle), he won the FA Cup in 1895[2] and claimed three Football League titles in 1893–94, 1895–96 and 1896–97,[3] although by the latter season he was no longer a regular, possibly due to injury – coincidentally the man who took his place in the side, Albert Evans, was another player from Barnard Castle, situated about 170 miles (270 km) from Birmingham; his absence meant he missed out on the rare opportunity to become a 'double' winner as he took no part in the 1897 FA Cup Final victory.

From Aston Villa Welford moved to Celtic in Scotland,[1] being enticed north along with teammates John Campbell and Jack Reynolds.

He played for Celtic for three seasons and won the Scottish Football League in 1897–98, followed by the Scottish Cup in 1899,[4] followed swiftly by the Glasgow Merchants Charity Cup, both knockout trophies won by way of 2–0 victories over local rivals Rangers.

[6][7] Welford made his debut for Durham in the 1895 Minor Counties Championship against Cheshire.