A snippet of info, that might help - or hinder.
The Parson & White Trade Directory of 1827 includes a page on business etc within Norham Parish.
Longridge and Horncliff(e) were two of the eleven "townships" that comprised
Norham Parish
James Paxton Gentleman, Horncliff
Inns. Longridge Robert Paxton Ord Arms Velvet Hall
Inns Horncastle William Paxton The Salmon.
No Paxton farmers listed for Norham Parish area.
Armstrong's Map of 1769 and Fryer's of 1820, show Horncliff, Longridge and Velvet Hall.
(Source- on line. Northumberland Communities site. communities.northumberland.gov.uk
Trade Directory within "Cornhill" community, under "Printed Material" section
Maps within "Berwick" or "Cornhill" communities, under " Plans" sections. )
One of the Paxtons of Horncliff, like the Scottish doctor Paxton, also had a dtr called Agnes in 1840s.
Trivia Angle
Velvet Hall had it's own railway station as early as 1849. On the Tweedmouth><Kelso line. Velvet Hall st closed 1955.
Michael