On the river side of Whitehall, the first floor (second to Americans), roughly parallel to the river. So called because of the mats covering the floor. For those with business at the palace, it was a convenient semi-private walk. The Duke of York’s closet and chief apartments were reached from it in the 1660s, with subsidiary rooms belonging to him on the floor below. Beneath it was the (equally long and thin) Stone Gallery.
The area shown on the map is approximate, based on this 1680 map and pp.480-1 of the Latham & Matthews Companion.