The coat of arms displayed on the walls of the Surrey Arms pub are for the county of Surrey. These arms were in use from 8th August 1934, and were replaced on September 20, 1974.
The description or blazon of these arms :
Per pale Azure and Sable a Fess per pale Ermine and Or in chief a representation of the Crown of King Edgar proper and a Sprig of Oak fructed Argent.
King Edgar, as well as several other Saxon kings, were crowned in Kingston. The ermine underneath the crown is from the arms of the Borough of Richmond. When Kingston and Richmond became part of Greater London, they left Surrey and so these arms were changed.
The sprig of oak and the colours azure and sable (blue and black) have been retained on the current arms for Surrey, see the Heraldry of the World website.