Thomas Arthur Fitton was born in Rhodes, Middleton, Lancashire, England in 1864. He began practising as an architect in Middleton in the late 1880s and gave Architect as occupation in the 1891 England and Wales Census, however, it is not known where or with whom he trained in the profession. He practised alone until 1921 when he took his son, Roderick Arthur Fitton (895-1977) into partnership as T. A. Fitton & Son.
The address of the practice was given as Winter Buildings 32 St Ann’s Street, Manchester in 1895; 29 Corporation Street, Manchester from 1903 to 1911; and 19a Corporation Street, Manchester in 1929. Thomas A Fitton's address was given as 8 Brown Street, Middleton, Lancashire in 1891; Park Road, Chester, Cheshire in 1901; Abbotsford Lodge, Manchester Road, Timperley, Lancashire in 1911; and Alkrington Green, Alkrington, Middleton, Lancashire in 1924 and 1929. He died on 17 February 1929.
Fitton's earliest known work was a cricket pavilion in Middleton (1890). Subsequent work by Fitton and Fitton & Son included a shelter at Middleton Cemetery (1891); Wesleyan Schools in Marple, Lancashire (1893); the conversion of the Lyric Theatre in Morecambe, Lancashire into public baths (1898); the Picture Theatre on Stamford New Road, Altrincham, Lancashire (1913); the Garden Village in Alkrington, Middleton (1913-19); premises for the Middleton and Tonge Co-operative Land and Building Society in Middleton (1925); the conversion of a foundry on Sussex Street, Lower Broughton, Salford, Lancashire into the Raincoat Factory (1928); offices, factory and warehouse for the Waterdale Dye Works in Prestwich, Lancashire (1929); a branch of the Union Bank of Manchester Limited on Ashton New Road/Grey Mare Lane, Manchester (1930); a bakery on Allison Street, Cheetham, Manchester (1930); and the Country Club and Lido on Buxton Road, Hazel Grove, Lancashire (1934). The practice also designed numerous private and municipal houses in Middleton, Darlington and elsewhere.