I assume you're referring to the typeface labeled “Two Lines English Egyptian” and shown in Caslon type specimen books in the early 1800s.
Photo by Oli Sorsby, 2013
“Two Lines English” refers only to the size of the type, so the design name is simply “Egyptian”. It is therefore often called “Caslon’s Egyptian”. Here is everything I know about the design, as we have documented on Fonts In Use:
All caps, designed circa 1816 and produced by Caslon IV. Widely regarded as the first commercial sans serif printing type.
Blake, Garnett & Co. (predecessor to Stephenson Blake) bought the matrices. It is shown in their specimen book ca. 1819, and a relaunched version appeared in the 1830s. [Mosely]
Digitized and expanded with a lowercase by Font Bureau as Caslon’s Egyptian. Also revived as a private project in 2013 by Jonathan Martin.
Martin’s revival, which involved inventing 12 missing characters, is shown below:
I’m not sure if a font of the original metal type still exists, but matrices (molds for making fonts) could be around because the type was recast for Ornamented Types around 1992.
I would check The St Bride Library in London.
Update: The complete original alphabet does still exist! In his new book Johnston & Gill, Mark Ovenden confirms that Ian Mortimer and James Mosely found complete matrices of the original font in the drawers of the Stephenson Blake Foundry (Caslon’s successor). They used these moulds to cast the type used in Ornamented Types.