A 'counter' table is the name given to a table which originally had the top marked out for calculating accounts (with lines and squares) and whose top slid open, allowing the coins that had been counted to be swept into the interior. It is common to find these tables have had their lids hinged (as here) or replaced.
A related counter table is illustrated in Wolsey and Luff Furniture in England, The Age of the Joiner, London, 1968, plate 122; and another in Ralph Edwards, The Dictionary of English Furniture, London, 1954, Vol ii, pg. 147, fig.3, which was sold in The Peter Gwynn Collection, Sotheby's, 27 November 2001, Lot 32. More recently a similar chest sold in 'The Property of H.W.Keil of Broadway' Christie's, 13 March 2007, Lot 18.