Born in Dulwich but grew up in Brixton. He first got into music after hearing Rock Around the Clock by Bill Haley and the Comets. He then listened to Jerry Lee Lewis, Little Richard, Fats Domino, Chuck Berry and Elvis Presley before turning on to blues musicians like Bo Diddley, Muddy Waters, Lightnin' Hopkins and John Lee Hooker.

At the age of 16, he bought his first guitar and, with his brother on drums, gathered other musicians and formed a band that played its first party in 1963. After undergoing a series of name changes, the group (whose membership included Chris Youlden) eventually settled on the name the Cross Ties Blues Band. By 1966, they had become the Lonesome Jax Blues Band, named after Peverett's first stage name. The band played the London club circuit and colleges.

Later, Peverett joined the Swiss blues group Les Questions, with which he played until October 1967, at which point he returned to the UK planning to start a band with Youlden. Instead, he joined Savoy Brown. After leaving Savoy Brown in 1970, Peverett formed Foghat with Roger Earl and Tony Stevens.