I've done a bit of laning around the NE this year, mainly with guided tours but a few independently and know a few of the lanes that are driveable without too much chance of getting stuck. northumberland council has a good interactive map of all open byways but if you dont know them it can be a bit dodgy on your own. if anyone fancies a day out let me know.
alternatively if you havent been before allterraintours.co.uk and uklandroverevents.com are NE based guided tour operators and offer a good day out for under £50