Kaiv, taking the road from Barnard Castle to Hexham that late in your journey is not a good idea. you will be tired/fatigued and those roads are not for the faint hearted at the best of times. my advice would be to take the A68 and take it easy.
my experience with long journeys (i do 300+ every sunday on small twisty roads) is that the closer you get to your end destination the more you want to push on and this is where mistakes happen. however if your a seasoned long journey rider then bash on