The King’s Mews (stables), Charing Cross, was on the site where the National Gallery now stands in Trafalgar Square. By 1820, horses were no longer stabled there and the building was instead used to exhibit mechanical arts and manufactures. It is not clear why it and for how long it was closed.

See http://www.architecture.com/Whatson/Exhibitions/ AttheVictoriaandAlbertMuseum/Architecturegallery/Buildingsincontext/ KingsMews.aspx and http://www.nationalgallery.org.uk/about/history/building/1833_400.htm and http://www.oldlondonmaps.com/viewspages/0225.html.