In reply to Lynsety:
There are several gotchas. You can't take bikes on the metro from Tynemouth, so you have to cycle back to Newcastle station (10 miles or so). You are supposed to book bikes on the Newcastle to Carlisle train. However, there are a reasonable number of spaces, so you will probably be OK. The train from Carlisle to Whitehaven only has 3? bike spaces and you can't book in advance. If you are lucky, like me, the conductor will let you sit with your bike at he end of the corridor. However, there are no guarantees.
For a major cycle touring route, the public transport options for getting back to the start are laughable.