Edmunds was born in Cardiff, Wales and played in a series of bands before launching a solo career in 1970(!) That year, his cover of "I Hear You Knocking" became a #1 hit in the UK (#4 in the U.S.). Edmunds also became a notable producer, which led to a working relationship with Nick Lowe. While legal issues prevented the use of the Rockpile name (Edmunds and Lowe were signed to two different labels), most of their work from 1976 through 1981 was as Rockpile (with Billy Bremner on guitar and Terry Williams on drums). Ironically, the one 'official' Rockpile LP came at the end of this period.
"Slipping Away" is off Edmunds' 1983 Information LP, which was released after Rockpile broke up. The song would go on to become a top 40 hit for him (barely), reaching #39 on the charts, while album rose to #51. I suspect that some of this success was due to the video, which received a bit of airplay on MTV back in the day.
Edmunds remains active in the music industry to the present day, although his work has been less frequent since the early 1990's.
Cool trivia fact: "Slipping Away" was written and produced by Jeff Lynne (of ELO fame).