Keep going. I do 'credit card' tours (i.e. I've booked my accommodation), so if I don't keep going the whole plan is messed up.
Worst rain was the hilly day of the C2C!
Edit: should have said, there were no stations nearer than the place I was aiming for, and even if there was, it would probably not have been possible to get to my next destination without touring the entire north of England!