AN ENGLISH CARVED AND PAINTED WOOD COAT-OF-ARMS

The possible matches for the arms are Long of Westminster, formerly Wroxall, recorded in the Wiltshire visitation Pedigrees of 1565 and 1623. John Edmonston's Complete body of heraldry 1780 attributes these arms of the Wroxall Longs to the Whaddon and Westminster baronets.
The other possibility is the Long family of Wiltshire from the late 15th Century, (Burke's Extinct Dormant Baroneties 1844)