Burrows found it impossible to force his way into the Wednesday side at left half, initially being kept out by Gavin Malloch. He eventually made his debut on 27 December 1932 against Manchester City and became Wednesday's regular left half for the next six seasons up to the outbreak of World War II. He played in 136 consecutive games for Wednesday from April 1933 till March 1936. This sequence of games included Wednesday's FA Cup run in 1935 when they lifted the trophy. He was also capped three times by England in this period, being first called up in May 1934 against Hungary. Subsequent internationals followed against Czechoslovakia and Holland before he lost out to Wilf Copping in the national side.