I was aware of a line to Consett at one time but I wouldn't have been able to tell you exactly when passenger services ceased. As you say, it does make you contemplate to what extent the effect of reopening the line would have on the local public transport infrastructure. It would have revolutionised transport across this large swathe of County Durham.
This is an excellent page about the rail service from Consett. It includes photos, details of the freight trains that typically operated, and timings of the last passenger service. Well worth a read
http://www.derbysulzers.com/24102.html