Gillows' design for this handsome desk was one of many published in the firm's sketchbooks under the heading Ferguson & Co, William Ferguson being one of the trio of former employees who purchased the Gillow business when the family relinquished control in 1813, the new partnership being known variously as Gillow & Co., Ferguson, Whiteside & Redmayne, or Ferguson, Redmayne & Co.
Ferguson and Henry Whiteside were responsible for the running of Gillow's London business based at various Oxford Street addresses until their deaths in 1835 and 1832 respectively.
The signature is that of William Barrow Sr, named on Gillow & Co.'s payroll in 1835, or possibly his son, also William, who was apprenticed to Redmayne in 1829 and became a freeman in 1837 (Susan Stuart, Gillows of Lancaster and London, 2008, vol.II, p.215).
A closely related desk is illustrated op. cit p.379, pl.GC32. Another was sold Christie's, London, 29 April 2010, lot 170 (£11,875 including premium)