Hi Howard,
Back home now. The article I mentioned is in "Publications of the THoresby Society", Vol. 61, Part 1, pages 1-26 (1978), and is entitled :"Fair Befall the Flax Field": Aspects of the Histroy of the Boyle Family and their Flax Business" by M.B. Boyle.
A brief precis ... Boyle Carr & Co. operated 1836-40 in Jack Lane Mill and Hunslet Lane (Gill was another of the partners). It then became Boyle Gill & Co., 1840-1853, based at Trafalgar Mill, Meadow Lane. The mill employed around 200 people by 1850, with salaries ranging from 4s. 3d. for doffers for a 60-hour week up to 20 - 30s. for supervisors.
Boyle Gill & Co. went bankrupt in 1853 - at the same time as numerous other mills, it seems, during a lengthy recession in the flax trade, but Boyle & Son was established the same year, based at Trafalgar Row, then later Mill Hill, and finally (up to 1964) at West Park Ring Road.
This company prospered, buying other properties, including, in 1878, Fell Beck Mill in Pateley Bridge, where my gt-gt-grandfather, William Noble was manager.
Even if there are no links to your family, the article provides some interesting social information about the flax industry in Leeds in the mid-19th century.
All the best
Tim