The branchline wasn't to the LD&ECR, it was, as I understand it, an industrial line which served various premises the first of which was Bryan Donkin engineers (were they the same ones used to make gas meters I believe?). It then continued roughly in the area now occupied by Ravenside retail park alongside the A619, serving several other properties I believe. Doing this from memory having read something about it somewhere, it terminated possibly at a brewery, the gateway to which is, or was still in place fairly recently in the vicinity of WD models.
I believe this is the gateway:
https://www.google.co.uk/maps/dir//Baslow+Rd,+Holymoorside,+Chesterfield,+Derbyshire+S42/@53.235656,-1.438098,3a,75y,90t/data=!3m8!1e2!3m6!1s-rQ7sp32t_po%2FVODCBB2oHkI%2FAAAAAAABhAI%2FQofX4C0wPNI!2e4!3e12!6s%2F%2Flh6.googleusercontent.com%2F-rQ7sp32t_po%2FVODCBB2oHkI%2FAAAAAAABhAI%2FQofX4C0wPNI%2Fs203-k-no%2F!7i4000!8i3000!4m8!4m7!1m0!1m5!1m1!1s0x487985dc26c69e31:0xd60c3f9f0c5187c9!2m2!1d-1.4909894!2d53.2302791
Edit;
looking at the things on the surrounding fancy ironwork, I reckon it's got to have a railway connection!