 Albion won the Football League title in 1919 – 20 for the only time in their history following the end of the First World War , their totals of 104 goals and 60 points both breaking the previous league records . The team finished as Division One runners @-@ up in 1924 – 25 , narrowly losing out to Huddersfield Town , but were relegated in 1926 – 27 . In 1930 – 31 they won promotion as well as the FA Cup , beating Birmingham 2 – 1 in the final . The " Double " of winning the FA Cup and promotion has not been achieved before or since . Albion reached the final again in 1935 , losing to Sheffield Wednesday , but were relegated three years later . They gained promotion in 1948 – 49 , and there followed the club 's longest unbroken spell in the top flight of English football , a total of 24 years . 
