I found this listing in the 'Esher News & Mail' dated 30th May 1958:
Music Box 83a High Street, Esher 3001.
… and this announcement in the 24th September 1965 edition:
MUSIC BOX TO CLOSE. The only shop in Esher catering solely for the needs of the record buyer is closing. It is the “Music Box” next to the post office in the High Street, which Mr John Bedford-Williams ran for almost seven years. Mr Bedford-Williams, who has sold the lease, says he does not know what sort of business the new owners have in mind. “They will not be selling records however,” he told our reporter. Now he is busy making plans for opening another business elsewhere, perhaps in Woking, combining records with possibly photography, which he is also keenly interested.