if you can hold a steady 90(shouldn't be too hard from glasgow to carlisle) id say about 5 1/2 hours tops.used to do sheffield to glasgow in four hours in a mercedes sprinter limited to 76mph.and i have done pod to sheffield in 1 1/2 hours at 90mph.
usually go glasgow,carlisle,penrith.across a66 to scotch corner and straight down a1/m1.
not sure how long going straight down the m6 to the m1.probably quicker at a guess as its all motorway.