Beamish was signed by Gordon Lee's Blackburn Rovers for a £25,000 fee in May 1974. He soon built a good understanding with strike partner Don Martin. The 1974–75 season was successful, as Blackburn were promoted to the Second Division as champions of the Third Division, with Beamish claiming 11 of he and Martin's 26 goal haul. Rovers finished mid-table in 1975–76 under the stewardship of Jim Smith. A popular player, fans would chant "Beamo, Beamo" years after he left Ewood Park.