That would be the Pantiles, a Georgian Colonnade which is essentially a long walkway with overhead columns that intersect into their entablatures, which are a superstructure consisting of moldings and bands that lie above the columns.
The area does indeed sound like it should be part of your roof, because "Pantiles" taken out of this context and application are essentially a kiln-fired roof tile made of clay, usually S shaped to overlap and fit sequentially to one another.
The Pantile walks were constructed in 1638 to provide lodgings and accommodations for the Royalty and influential people who were bathing in the adjoining Chalybeate Spring, a natural mineral spring with a high content of Iron salts, thought to be therapeutic and prolong life.
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