The campaign, led by the British Phonographic Industry, is in response to a legal loophole effective Jan. 1, 2005, allowing copies of music to be made 50 years after its original release without paying royalties to the copyright owner, the BBC reported Monday.
Presley's "That's All Right" and "Shake, Rattle and Roll" by Bill Haley and the Comets will be among the first to expire in January under the current law.
During the next few years, many rock classics could become public domain, including hits by Little Richard, Fats Domino and Bo Diddley.
The Beatles' songs would begin expiring Jan. 1, 2013, with the first single "Love Me Do." The entire catalog would expire over the next eight years.
Copyright protection in the United States exists for 95 years after a song is released, Australia and Brazil have 70-year terms and India has 60-year terms.