Teulon was born in 1812 in Greenwich, Kent, the son of a cabinet-maker from a French Huguenot family. His younger brother William Milford Teulon (1823–1900) also became an architect.
He was articled to George Legg, and later worked as an assistant to the Bermondsey-based architect George Porter. He also studied in the drawing schools of the Royal Academy. He set up his own independent practice in 1838, and in 1840 won the competition to design some almshouses for the Dyers' Company at Ball's Pond, Islington. After this his practice expanded rapidly. During the next few years his works mainly consisted of parish schools, parsonages and similar buildings, mostly in the Home Counties.
He was a friend of George Gilbert Scott and became a member of the Council of the Royal Institute of British Architects on 6 January 1835. Between 1841 and 1842 he undertook a long study tour of continental Europe with Ewan Christian who remained a lifelong friend and became his executor. Also in company during the tour was Horace Jones who was later knighted and became architect to the Corporation of the City of London and Hayter Lewis, later Professor of Architecture at University College, London.
He built his first church, the Early English-style St Paul, Bermondsey, in 1846. Soon after this he designed St Stephen, Southwark, a building adapted to its square site by being planned in the form of a Greek cross, with the recessed angles filled in by the tower, vestry, chancel aisles. Teulon's religious views were Low Church, and his patrons were predominantly members of established aristocratic families who shared his outlook. In 1848 he received a commission from the 7th Duke of Bedford to design cottages for the Thorney estate, and the next year he built Tortworth Court, Gloucestershire, a substantial mansion in a kind of Neo-Tudor style, with a large central tower, for the Earl of Ducie. Other clients included John Sumner, archbishop of Canterbury, who commissioned Christ Church in Croydon; the Duke of Marlborough, for whom he refitted the chapel at Blenheim Palace in 1857-9; the 10th Duke of St Albans and Prince Albert.
His work included the remodelling of several unfashionable 18th-century churches to suit contemporary tastes. Archibald Tait, the Bishop of London, praised his alterations at St. Mary's, Ealing, as "the transformation of a Georgian monstrosity into the semblance of a Byzantine Basilica".
As well as Gothic Revival churches, he designed several country houses and even complete villages, as he did at Hunstanworth in County Durham in 1863.
Despite his classical training, Teulon's early designs were mostly in imitation of Tudor and Elizabethan styles, and he soon became an enthusiastic follower of the latest developments of the Gothic Revival. He was an enthusiastic user of Polychrome brickwork. His planning was often elaborate: Henry-Russell Hitchcock called his mansion at Elvetham Park in Hampshire "so complex in its composition and so varied in its detailing that it quite defies description". Some of his later work was, however more restrained: for instance at St Stephen's Church, Rosslyn Hill, Hampstead, (1869–76) the exterior is of purple-brown brick, of subtly varied tones with light stone trimming. The massing of the building is also simpler than in his earlier designs.
Teulon died at his home in Hampstead on 2 May 1873 and was buried in Highgate Cemetery. His great great great nephew, Alan Teulon, published a book on S.S. Teulon in 2009. He was survived by four sons and four daughters.
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St James's Vicarage, Chipping Campden, Gloucestershire; additional wing 1844 (now demolished)St Mary's Rectory, North Creake, Norfolk; 1845Holkham Hall, Norfolk, porch 1847St Paul's Parish Church, Bermondsey; 1848 (demolished 1961)All Saints' Parish Church, Icklesham, East Sussex; restoration 1848–49Church of the Holy Spirit, Rye Harbour, East Sussex; 1848–49Owlpen House, Owlpen, Gloucestershire; 1848 (demolished 1955-6, apart from the stables and lodge)Thorney Model Village, Cambridgeshire; from 1848St Mary's Parish Church, Pakenham, Suffolk; alterations 1849Queen's Terrace, Windsor, Berkshire; 1849St Paul's Church, Sandgate, Kent; 1849St Peter's Church, Great Birch, Essex; 1849–50Tortworth Court, Tortworth, Gloucestershire; 1849–52St John's Parish Church, Rushford, Norfolk; restoration c.1850St Mary's Parish Church, Benwick, Cambridgeshire; 1850 (now demolished)St Mary's Parsonage, Grendon, Northamptonshire; 1850St Stephen's Parish Church, Manciple Street, Southwark; 1859 (demolished 1965)St John's Parish Church, Kingscote, Gloucestershire; restoration 1851Christ Church, Croydon, Surrey; 1851–1852 (largely destroyed 1985)Holy Trinity Parish Church, Hastings, East Sussex; rebuilding 1851–59St Andrew's Parish Church, Brettenham, Norfolk; restorations and remodelling 1852 St James' Church, Edgbaston, Birmingham; 1852St Margaret's Parish Church, Angmering, West Sussex; restoration 1852–53St John's Church, Ladywood, Birmingham; 1852–54Estate cottages, Windsor, Berkshire; 1853School in Oxford Road, Woodstock, Oxfordshire; 1854A cottage, Tortworth, Gloucestershire; 1854Sandringham House, Norfolk, porch and conservatory 1854Cholmondeley Castle, Cheshire; alterations 1854Schoolmaster's house and chapel, Curridge, Berkshire; 1854–55Christ Church Parish Church, Fosbury, Wiltshire; 1854–56St Andrew's Parish Church, Lambeth, London; 1855St Mary's Vicarage, Steeple Barton, Oxfordshire; 1856St John the Baptist's Parish Church, Burringham, Lincolnshire; 1856–57St Mary's Parish Church, Sunbury, Surrey; internal alterations 1857St Thomas's Church, Pearman Street, Lambeth; 1857 (demolished)Shadwell Park, Rushford, Norfolk; extensions & remodelling 1857–60All Saints' Parish Church, Wordwell, Suffolk; restoration 1857 and 1866St Giles's Parish Church, Uley, Gloucestershire; rebuilding 1857–58St Mary's Parish Church, Alderbury, Wiltshire; 1857–58Holy Trinity Parish Church, Oare, Wiltshire; 1857–58All Saints' Parish Church, Middleton Stoney, Oxfordshire; rebuilding 1858St Bartholomew's Parish Church, Newington Bagpath, Gloucestershire; rebuilt chancel 1858Browne's Charity Almshouses and Chapel, South Weald, Essex 1858St James's Parish Church, Leckhampstead, Berkshire; 1858–60Prince Albert's Workshops, Windsor Great Park, Berkshire; 1858–61St John the Baptist's Parish Church, Netherfield, East Sussex; 1859Christ Church, Wimbledon, London; 1859–60Elvetham Hall, Hartley Wintney, Hampshire; 1859–60Hawkleyhurst House, Hawkley, Hampshire; 1860St Mary's Vicarage, Gainford, County Durham; 1860St Silas' Church, Penton Street, Islington; 1860, completed 1863 by E.P. Loftus BrockSt Bartholomew's Parish Church, Nympsfield, Gloucestershire; rebuilt church 1861–63St Mark's Parish Church, Silvertown, London; 1861–62 (now the Brick Lane Music Hall)Huntley Manor, Huntley, Gloucestershire; 1862Bestwood Lodge, Bestwood, Nottinghamshire; 1862–65St John the Baptist's Parish Church, Huntley, Gloucestershire; 1863Village of Hunstanworth, County Durham; 1863St Thomas's Parish Church, Camden, London; 1863 (now demolished)All Saints Church, Benhilton, Benhilton, Sutton, Surrey; 1863St Mary's Parish Church, Woodchester, Gloucestershire; 1863–64Royal Chapel of All Saints, Windsor Great Park, Berkshire; 1863–66St Peter and St Paul's Parish Church, Hawkley, Hampshire; 1865St Mary's Parish Church, Horsham, Sussex; south aisle 1865Wrotham Park, Hertfordshire; alterations 1865St George's Parish Church, Hanworth, Middlesex; spire 1865Buxton Memorial Fountain in Victoria Tower Gardens, London; 1865Tyndale Monument, North Nibley, Gloucestershire; 1866St Paul's Parish Church, Greenwich; 1866St Margaret's Parish Church, Hopton-on-Sea, Norfolk; 1866-7St Mary's Parish Church, Ealing, London; 1866–73St Andrew's and St John's School, Roupell Street, Lambeth; c.1868Lychgate to Church of St. Peter, South Weald, Essex 1868Church of St. Peter, South Weald, Essex 1868St Stephen's Parish Church, Rosslyn Hill, Hampstead, London; 1869-71The Court House, St Andrew Holborn, London; 1870St John the Baptist's Parish Church, Windsor, Berkshire; alterations 1869–73Woodlands Vale House, Ryde, Isle of Wight; 1870–71St Frideswide's Parish Church, New Osney, Oxford; 1870–72Holy Trinity Parish Church, Leicester; remodelling 1871St Andrew's Parish Church, Eastern Green, Coventry; 1875Embrook House, Sandgate, Kent; 1852 (demolished)Riseholme Hall, Stable block (perhaps) Riseholme, Lincolnshire 1840–45St Mary's Church, Riseholme, Lincolnshire 1851