I saw the National Rail pdf, but don't know if those work for Cragside and Rothbury. For example, Alnmouth Station Taxis seems to have become Knights Taxis, whose website did not make it sound as if they are a large operation, which could mean not having taxis available when we want them. Or maybe they do.

Do you have any experience with any of these companies?

Pronounce as Anick and and Alnmouth?