I can’t help you with a lift but if you come on the ferry to Newcastle I assume you’ll arrive in Tynemouth. It is a shortish ride to Newcastle central station using one of the National cycle networks along the river.
From Newcastle you can get the train to Whitehaven via Carlisle. In theory both trains take bikes but space is limited and it is done on a first com first served basis. It is free to take bikes on. I have never had an issue as even when there were too many bikes if the train is not full then the ticket inspectors let you on.
The train isn’t that expensive and you can buy in advance using http://www.thetrainline.co.uk.
Other options for Newcastle are to try Newcastle Mountain Bike Club or one of the various face book groups in the area such as cycling around Tyne and Wear