Layout of Derby in 1990 (London Midland Region Track Diagrams, Quail Map Company, October 1990) attached; I don't know how much had changed since the 1969 resignalling. Prior to that, there was an avoiding line which the Blue Pullman used, north via Chaddesden South Junction, past Chaddesden Sidings, whence to Duffield [Derby South Junction to Derby North Junction], and the route had an option to run into Derby from the north end as well by turning left instead of right [Derby South Junction to Derby Junction], and I've got a 1968 working timetable showing passenger trains using primarily the latter route back to the station which allows trains to run Nottingham-Tamworth without reversing. I don't have a timetable showing the Master Cutler passing Derby without stopping.
Others have already said that the avoiding line via Chaddesden was removed as part of the 1969 resignalling.