Using Google Books, I found several references to this company:List of members
By Institute of Taxation, Institution of Civil Engineers (Great Britain)-1896
Journal of the Institute of Bankers
HS King & Co 65 Cornhill EC За Victoria Street SW
By Institute of Bankers (Great Britain)-1887
No 155 was occupied by Messrs Smith Elder and Co in 18G7 who have since become Messrs HS King and Co who still carry on their business at this house.
They appear to have been involved in publishing or book sales and are referenced as agents for the sale of books published by the Superintendent of Government Printing, India.
And another hit, this one from London Gazette Issue 27529 published on the 25 February 1903:
Sir Henry Seymour King, K.C.I.E., M.P.
Names of Places where the Business is carried on.
This is a very curious trail...