William S. Hammersley “was a manufacturer of chinaware in England, which business he followed until 1843, in which year he emigrated to America, locating in New York City, where he became an importer of china and earthenware.” When he made that transatlantic crossing on 20 May 1843, he seems to have come alone, with his family to follow sometime later.
The ship he came on was the Thomas P. Cope:
The Thomas P. Cope was a packet ship that sailed between Philadelphia and Liverpool, making 21 round-trip voyages between 1839 and 1846. In December 1846 the ship was struck by lightning and burned for six days before sinking. (source)