Excellent photographic quality shots.
In the upper shot of IanOHoseason's post Q6 63405 appears to be coming off the Lanchester Valley branch (Consett South Jcn - Lanchester - Witton Gilbert - Baxter Wood Jcn - Relly Mill Jcn), taking the chord for Baxter Wood No2 SB and joining the ECML Up line at Bridge House Jcn. I can't see the signal ahead of it, so alternatively it could be intending to take the connection up to Deerness Valley Jcn, a lesser used route which could take it to the Up ECML via Bishop Auckland, Shildon and Darlington North Road. Deerness valley Jcn would also give access to the Waterhouses branch. If it needs water, the Q6 could pause just short of Deerness Valley Jcn and use the water crane just to the north of the stone bridge which spanned the lines.
In the lower shot, we appear to be facing the opposite direction, looking south. The Q6 0-8-0 appears to be coming off the chord from Bridge House Jcn, so the train has come from the ECML Down line. The lines to the left are from Durham, leaving the ECML at via Relly Mill Jcn. The fireman will be shovelling coal to keep steam pressure up after the climb from Bridge House Junction. The gradients will ease for the run to Lanchester, but will increase sharply for the run between Lanchester and Consett South Jcn.
In both shots the hoppers could be either loaded or empty! The steel works at Consett had a voracious appetite for coal and coke, which could reach Consett Low yard from the South via the Lanchester Valley branch, from the east via South Pelaw Jcn or from the north via the Derwent Valley branch. However, the colliery at Bear Park was still operational in the 1950s and could be either sending coal or coke towards Tees-side via Ferryhill or receiving empties from Ferryhill.