We did it the other way, Cumbria to Yorkshire (going home!) ..
But can send a route. We camped Twice, once at Kirkby Stephen and once at Thirsk ish ... However, I don't know the viability of the route totally now as it all changes, with regards to legality and TRO's. At the time we did it, it was OK. There's a right mix of every type of lane in UK .. grass, farm track, rocky mountain trail, to boggy marshland, to river crossings to high moorland, it's a great trip ..
Message me with an email and I'll send a route and the itinerary I drafted, it should help a little .. Actually just noticed upload a file button .. see if it works ..
OK, it's sent the PDF but won't include the Memory Map track so send me a meassage and I'll email it.
Bear in mind, the pdf is what was planned, as is the route .. but both changed as circumstances dictated. We didn't stay at Robin Hoods Bay, indeed we went to Scarborough instead, cutting a few of the later lanes out due to breakdowns and time .. but they'll give you an idea.