Beaumont Asquith was born in Painthorpe, near Wakefield, on 16th September 1910. After playing local football he joined Barnsley in July 1933. At the time the club played in the Second Division of the Football League.
Asquith initially played in the team as an inside-left. He was switched to left-half but it was not until he settled down as a centre-forward that he fulfilled his true potential. However, in the 1937-38 season Asquith was unable to save Barnsley from being relegated from the Second Division.
Asquith was signed by Manchester United in May 1939. During his time at Barnsley he had scored 40 goals in 105 games. However, he only played in one game for his new club before the outbreak of the Second World War. During the conflict Asquith guested for Blackburn Rovers, Huddersfield Town, Barnsley, Leeds United, Rotherham United, Doncaster Rovers and Bradford City.
Beaumont Asquith died in Barnsley on 12th April 1977.