Hampson was the middle of the three Hampson brothers who played for Leeds City during the First World War; the oldest was full-back Billy and the youngest goalkeeper Tommy. The three were unrelated to the other two Hampsons, brothers E and Jack. There were often three or four Hampsons in the City side during the 1917/18 season and Tommy, Walker and Billy played in the same City eleven three times in April.

Though normally a wing-half, all Walker's three games for City came as a full-back partnering Billy.

Walker saw service with Black Lane St Andrews and Colne before he was signed by FA Cup holders Burnley for whom he played four First Division games in 1914/15.

Walker was given the opportunity of guesting for Leeds City in April 1918 and the attraction of playing for his brothers secured his services. His first game came in a 2-1 victory at Bradford Park Avenue on 6 April and he kept his place for the two goalless draws that followed against Bradford City. The man he had replaced, Harry Millership, returned for the two-legged championship play off games with Stoke in May.

Hampson joined non-league Scotswood for a while but signed for Second Division South Shields in 1919 and played 49 Second Division games for them over the next couple of years. He joined Charlton Athletic in 1921 and then moved back to the North East for a year with Hartlepools United and then had a season with Chesterfield. He had trials with Rochdale and Grimsby Town thereafter but never made it into their first teams.

He died in 1959.