Longmuir was born at Simpson Memorial Maternity Pavilion Hospital, Edinburgh, and is the elder brother of the group's drummer, Derek Longmuir. In 1976, at the height of the band's popularity, Alan Longmuir was replaced by rhythm guitarist Ian Mitchell, a man ten years his junior, who would in turn make way for Pat McGlynn. Tam Paton, then the group's manager, alleged that Longmuir had tried to commit suicide.
Longmuir returned to the group in 1978 following McGlynn's departure, and thereafter switched between bass guitar, rhythm guitar and keyboards. He also plays piano accordion.