He was a founder member of the group, best known for classic tracks Roll Away The Stone and All The Young Dudes.
The latter was written and produced by David Bowie, who sang backing vocals on the track.
The band, who made eight albums during their five-and-a-half year existence, reformed to mark their 40th anniversary in 2009 - but Griffin was too ill to take part.
The BBC reports he died peacefully in his sleep on Sunday night, said Peter Purnell from record label Angel Air records.
He called Griffin "one of the nicest, friendly and talented men I have ever known."