There's an entire book called The Mortimer Gunmakers by H. Lee Munson. There's a family of gunmakers over several generations.
Harvey Walklate Mortimer (1753-1819), Thomas Mortimer (1755-1824), Jackson Mortimer (1762-1834), Henry William Mortimer (1796- ), H.W. Mortimer Jr. (1776-1850), Thomas Jackson Mortimer (1781-1833). Someone said he made flintlocks. The family name as gunmakers spanned nearly 100-years and they made many caplocks, tubelocks and cartridge guns - until1923. At one time they were Mortimer and Sons. When the elder passed, they went back to Mortimer. Each primary was issued a Royal Warrant and used the logo "Gunmaker to His Majesty". The London guns were considered "Best" quality to the point that they were some fraudulent copies. I own a dueling pistol made by HW the senior, and a SxS shotgun made by T.J. I have previously owned a double rifle by Mortimer and Sons that is a breachloading .500 Express from 1880.
They had nothing to do with the American West. They sold face to face, or sent delivery by train, so they were not widespread in other Countries in Europe. Unless someone brought the gun back by ship, no guns were "exported" for sale. It is likely they never even heard of Hawken. The rifle they made popular is an English Sporting Rifle based on Gibbs, Boss and Mantons rifles.