The musician joined the Scottish pop band in 1976 when he was 17, to replace founding member and bassist Alan Longmuir.
Mitchell, who was from Northern Ireland, was the first band member born outside of Edinburgh, but left after seven months.
A statement on the band’s Instagram page said: “We are deeply saddened by the news of Ian Mitchell’s death. Our thoughts and prayers are with his wife Wendy, their family and friends. Rest In Peace, Ian.
“If you wish to leave your condolences, please do so in the comments below.”
During Mitchell’s time with the band, which has had many changes to the line-up, they released the 1976 album Dedication and a cover version of the Dusty Springfield song I Only Want to Be With You.
The tartan-clad band had previously dominated the charts with songs such as Saturday Night, Bye Bye Baby, Money Honey and I Only Want To Be With You, selling almost 300 million records worldwide.
As the group’s popularity waned, Mitchell quit the band and was replaced by guitarist Pat McGlynn.
Stuart ‘Woody’ Wood, who is among the founding members and still performs with the band, wrote on Facebook: “Very sad, sad news about Ian Mitchell. We’d like to send our love and condolences to Wendy and all Ian’s family and friends … you are in our hearts.
“I have many fond memories of Ian not only in the BCR days but also when we played together in the ’80s with The Passengers … great guys and great days! You will sorely be missed Ian … ”
The band’s current line-up features Ian Thomson on lead vocals and guitar, Marcus Cordock on bass guitar, Jamie McGrory on drums and Wood on guitar.
