Surely the most obvious influence on this recording is Robin Williamson, from both his Incredible String Band days and his later solo career. Just listen to the phrasing, for example, in "So Bored Was I." Not to mention the overall instrumental, melodic, and lyrical approach, forged like Williamson's in the Scots folk tradition and taken in unusual, albeit organic-sounding, directions.
Alasdair Roberts is someone whose music I'm just discovering, with undiluted delight. I also highly recommend his all-traditional "No Earthly Man."