Also, I've just checked on The AA Routeplanner, it reckons about 162 miles, putting average daily distance to about 33 miles per day (ie: about a further 1 hours' walking per day).
But that is using a lot of dual carriageways and motorways that might not be suitable for walking on, especially in the dark and possibly in poor weather. Roads without a pavement could be quite dangerous at that time of year.
Don't get me wrong - I'm not trying to dissuade you, but 33 miles per day in possibly poor conditions on dangerous and busy stretches of road might take some doing. Is it better to find a safer, if slightly longer, route, and maybe stretch to 6/7 days?