When World War II had begun in 1939 he had decided to join the Royal Australian Navy, which restricted his appearances for the club.

Bevan arrived on board HMAS Australia in Britain in 1946, and all he had with him was a letter of recommendation which was written by former Eastern Suburbs Test winger Bill Shankland.

[3] Bevan requested a trial with Leeds, which was a suggestion from Shankland, but the club decided against signing him partially due to his frail looking appearance.

Bevan was the 1947–48 Northern Rugby Football League season's top try scorer and also played for Warrington in their Championship final victory.

Bevan scored a try in Warrington's 8–14 defeat by Wigan in the 1948–49 Lancashire Cup Final during the 1948–49 season at Station Road, Swinton on Saturday 13 November 1948,[5] Brian Bevan played on the wing in Warrington's 19–0 victory over Widnes in the 1949–50 Challenge Cup Final during the 1949–50 season at Wembley Stadium, London on Saturday 6 May 1950 in front of a crowd of 94,249.

Bevan played for the British Empire XIII against New Zealand on Wednesday 23 January 1952 at Stamford Bridge in London.

Bevan played on the wing in the 8–4 victory over Halifax in the 1953–54 Challenge Cup Final replay at Odsal, Bradford on Wednesday 5 May 1954, in front of a record crowd of 102,575 or more.

He scored a try in Warrington's 5–4 victory over St. Helens in the 1959–60 Lancashire Cup Final during the 1959–60 season at Central Park, Wigan on Saturday 31 October 1959.

Bevan played most of his career in Britain, and was never selected to represent Australia in a test match, although he did mesmerise Kangaroo touring sides with his guile and skill for almost two decades.

[14][15] In June 2018, Bevan was named on a shortlist of ten players for potential induction into the NRL's The Immortals, with two to be selected and announced in August of the same year.

[16] While the NRL made a surprise announcement that they were making five inductions rather than the planned two on the night, Bevan was not among those raised to Immortal status.