Washington, County Durham born outside right Billy Thirlaway began his football career with Usworth Colliery in 1920 and was signed by Second Division West Ham United in the 1921 close season, making his Football League debut against Bradford Park Avenue the same August. He scored twice in 36 appearances during his debut season as West Ham finished 4th in the Second Division, but he lost his place at the start of the 1922-23 season and made only a further 3 starts for The Hammers over the next two seasons, before joining Southend United in the summer of 1924. He lost his place in the Southend line up in September 1924 after only 8 appearances, and joined Luton Town in February 1925, where he made 13 appearances before the end of the season.
He then joined Second Division South Shields in the 1925 close season, scoring 5 goals in 32 appearances before returning to the First Division with Birmingham the following summer, scoring once in 23 appearances in 1926-27 before being signed by Cardiff City in March 1927. He was cup tied for their FA Cup victory over Arsenal but played in the FA Charity Shield when they beat The Corinthians 2-1 at Stamford Bridge in October 1927. He scored 11 goals for Cardiff, missing only two games, as they finished 6th in the League Championship and continued as a first team regular beyond their relegation the following season, eventually leaving Ninian Park to join non league Tunbridge Wells Rangers in 1930 after 22 goals in 115 appearances for The Bluebirds. He then returned to Usworth Colliery in 1931 where he finished his career.