 Having a Rave Up was released before the advent of critical rock music journalism. A December 1965 staff review in Billboard indicated the album's potential to enter the Top LPs chart. Several retrospective reviews have been favourable. AllMusic's Eder gave the album four and a half out of five stars and describes it as "one of the best LPs of the entire British invasion, on a par with the greatest mid-1960s work of the Beatles and the Rolling Stones". Author Denise Sullivan noted, "Among British blues-rock albums, this Giorgio Gomelsky production is the pick for its wealth of hits and its influence on garage rock and hard rock lead guitar."
