I have not done the whole route, but, we have done the section of the coastal route between Berwick and Holy Island. There is video of our journey
here. It is full length, one direction, (opposite direction to your plan). It wasn't the best weather, and, we got a puncture, but, we (two 70+ year olds) managed it no problem. Not sure the type of bike you are planning to use, but, I would not think it is suitable for a road bike.
As
@Pale Rider has said, the Hadrians Way Cycle route into Newcastle from the west is good. There is also a route on the south side of the Tyne (Keelmans Way), which links to the North side, via a cycle/pedestrian tunnel under the Tyne at Jarrow. A word of warning if you do choose to take that route, the lifts are notoriously unreliable, and, carrying your bike up the stairs is not for the fainthearted, so, I would check their website before deciding north or south of river! There is video of the Eastern end of Hadrians Way, and Keelmans Way
here, again, it is quite lengthy, but, you can fast forward.
