Feilden was the third son of Joseph Feilden and Margaret Leyland of Witton. He was educated at Blackburn Grammar School and Brasenose College, Oxford. He became a cotton mill owner and lived at Witton Hall. In 1798 he purchased the hamlet of Feniscowles south west of Blackburn, from Thomas Ainsworth.
Feilden built the house of Feniscowles in Pleasington in a romantic valley on the banks of the River Darwen. He also gave a site for a church at Feniscowles in 1840, and provided the stone for its construction.
In 1841, Feilden changed his allegiance to the Conservatives but remained MP for Blackburn until 1847. He did nothing to distinguish himself in the House of Commons in his fourteen years as a M.P. He never spoke once and never took an active part in any parliamentary measures. In 1846, Feilden was created Baronet of Feniscowles.
Feilden died at the age of 78.
Feilden married Mary Haughton Jackson, daughter of Edmund Jackson, at St Martin in the Fields on 30 March 1797. They had three sons and three daughters. His son William succeeded to the baronetcy. Another son Montague Feilden also became MP for Blackburn.