No. The rapid growth of factories and mills in England during the Industrial Revolution (late 18th–19th century) did not cause a surge in English immigration to the U.S. In fact, English emigration had already begun declining by the late 1700s.
Major waves of English migration occurred earlier: 17th century (colonial settlement) and early 18th century. By the Industrial Revolution, England's growing economy absorbed labor domestically, and later Irish, German, and Southern/Eastern European immigrants dominated U.S. inflows.