The name Dukewilley appears in both the 1861 and 1851 censuses.
But in the 1841 census it is called ‘Duke William’.
There is no indication in any of those census returns of it being a public house at that time.
The earliest reference I can see, so far, in parish records is a baptism in 1805, where the place was also called ‘Duke William’.
There are some references to the house in historic newspapers, the earliest and most significant I have found so far was in The Bath Journal of 26 June 1809 which said:
‘On Saturday evening, the Duke William public house near Hexham, was burnt down, having been set on fire by some sparks from the chimney. The furniture was all saved’.
I will let you know if I find any more information which might help.