It is the former Lifeboat House, see link below. Think it may now be a ship's chandlers supplying bits for the yachties.
HISTORY: The Lifeboat House was built in 1866 by the Royal National Lifeboat Institution (RNLI), which had taken over the lifeboat service from the Dover Humane and Shipwreck Institution in 1855. The building was modified in the late 1870s to accomodate a bigger lifeboat.
The Clock Tower was built in 1876-7 to the designs of George Devey (1820-1886). The work was commissioned by the Dover Harbour Board, and following the completion of the Clock Tower, Devey was further commissioned to design a marine bathing establishment and to lay-out some adjacent building land. The building work was undertaken by a local builder, W.J. Adcock. The Clock Tower is all that remains of Devey's work, the rest being destroyed by shelling in World War II.
The Lifeboat House was originally orientated with its doors to the north, and Devey located the Clock Tower to the east of the Lifeboat House and linked the two buildings to the north with an archway. Devey created both a stylistic as well as physical link between the two buildings, giving the appearance of a complex, rather than two isolated structures. In 1892, construction started on the new Prince of Wales Pier so the Clock Tower and Lifeboat House, in the way of the new pier approach, were both carefully taken down and re-erected a very short distance away, but on a different alignment with one another. The connecting archway was lost at this time.