Kilnhurst, near Rotherham, Yorkshire born outside right Laurie Burkinshaw began his football career with Kilnhurst Town and played for Midland League club Mexborough Town in 1910, joining First Division club Sheffield Wednesday in 1911, where he made his Football League debut at Notts County that September, scoring on his home debut in a 4-0 win over Tottenham Hotspur a week later. A fringe player during much of his time at Hillsborough, he made 16 appearances during their 1913-14 campaign, after which he signed for Midland League club Rotherham Town in the summer of 1914 after 7 goals in 25 appearances for The Owls.
He soon moved on to Stalybridge Celtic but his career was then interrupted by the First World War, and after the War he joined Second Division club Birmingham in the summer of 1919, where he was a regular on the right wing for two seasons missing only 7 matches as they won the Second Division Championship in 1920-21. However in the top flight he played only 4 more matches for Birmingham and returned to Yorkshire joining Third Division (North) club Halifax Town in the summer of 1922 after 12 goals in 75 appearances for The Blues. In his single season at The Shay, he scored twice in 31 matches for Halifax Town, and re-joined Mexborough Town in 1923, his final known club before his eventual retirement.
His older brother was Jack Burkinshaw, and they played together for Sheffield Wednesday and Rotherham Town, Jack also played for Grimsby Town and Swindon Town before the War, Bradford Park Avenue and Accrington Stanley after it. Also Ralph Burkinshaw, who played most notably for Bury and Bradford City in the 1920’s, was his younger brother.