Shelley was born in Tiger Bay, Cardiff. In 1982, Shelley was reported to be a born-again Christian.
Shelley is often compared to Rush bassist/vocalist Geddy Lee, as they both share the position of bassist/vocalist in power trio bands, both have high pitched distinctive voices, and during the mid to late 1970s they bore a striking resemblance to one other, with long straight hair and huge glasses. Like Lee, Shelley possessed a high tenor vocal range.
Budgie's November 2010 tour of Eastern Europe had to be cancelled as Shelley was hospitalised on 9 November in Wejherowo, Poland, with a 6 cm aortic aneurysm. After surgery, he returned to Britain for recovery, but no decision about the future of the band has been made. Shelley has said that that following the operation he finds it hard to simultaneously sing and play bass guitar for long periods. Nevertheless, he continues to play bass (with occasional backing vocal duties) in rock and pop covers bands based in South Wales.