Reid is acknowledged by Robert Plant as the outstanding voice of his generation and an influence on Led Zeppelin's early material and is credited by Jimmy Page for connecting him to Robert Plant. Reid's early song "Rich Kid Blues" was covered on an album by Marianne Faithfull in 1984. The UK artist Rumer recorded "Brave Awakening" on her "Boys Don't Cry" 2012 album and appeared at his London shows at the Jazz Cafe and Half Moon. Cheap Trick recorded Reid's "Speak Now" for their 1977 album debut album. The Raconteurs with Jack White also recorded a version of Reid's "Rich Kid Blues" for their second album "Consolers of the Lonely" in 2008. The American rock group The Split Squad recorded a cover of Reid's "Tinker Taylor" for their debut album, "Now Hear This...", released in 2014. Joe Perry's album "Sweetzerland Manifesto", released in 2018, features three tracks co-written and sung by Reid. In 2020, a recording of Chris Cornell covering Reid's "To Be Treated Rite" was released on his posthumous album "No One Sings Like You Anymore, Vol. 1."