"The Star, Appleton" is mentioned several times in the Oxford Journal in the 1770s, in relation to auctions re. the sale of land/timber in the area. Those are the latest dates I can find.

From the same source -

"Mr White's Three Horseshoes, Appleton" - first mentioned 22 June 1833
"Mr Webb's Plough, Appleton" - first mentioned 22 February 1834

All these references relate to auctions being held there re. the sale of timber/land in the area.

Between the 1780s and 1830s "The Dog House, Marcham" or "The White Hart, Tubney" appear to handle this business