Sibford Gower parish includes the village of Burdrop. The 2011 UK census recorded the parish's population as 508.
A Quaker congregation was established in the village by 1669, when it met in the home of the clockmaker Thomas Gilkes. In 1678 or 1681 a Quaker meeting-house was built on land bought for the purpose by Bray D'Oyley, Thomas Fardon and Thomas Gilkes. By 1682 it had a burial ground. In 1736 a gallery was added inside the meeting-house to accommodate its growing congregation. The 1851 Census recorded that 112 people attended its Sunday meeting. In 1865 the old meeting-house was replaced with the present one southwest of the village, on the road to Hook Norton.
Sibford Gower was part of the Church of England parish of Swalcliffe until 1841, when a new ecclesiastical parish of Sibford Gower, with Sibford Ferris and Burdrop was created. The Church of England parish church of the Holy Trinity in Burdrop was built in 1840 to serve the new parish.
Sibford Gower became associated with clockmaking in the 17th century. Thomas Gilkes was born in Sibford Gower in about 1665 and pioneered clockmaking in north Oxfordshire. There is no known record of where he learnt his trade, but as he was a Quaker he would have been apprenticed to a fellow Quaker; possibly Richard Gilkes of the Worshipful Company of Clockmakers in London. Thomas Gilkes died in 1743.
Thomas Gilkes trained two of his sons as clockmakers: a third Thomas (1704–57), who then worked in Charlbury as both a clockmaker and a Quaker minister, and Richard (1715–87) who established his business in West Adderbury. John Fardon (1700–43) of Deddington also served his apprenticeship with the elder Thomas Gilkes in Sibford. Gilkes pioneered a clockmaking industry in north Oxfordshire villages with such success that his fellow-Quakers, including several further members of the Gilkes and Fardon families, dominated the trade in parts of the district for the next 150 years.
Later clockmakers in Sibford Gower were also Quakers. John Wells' date of birth is unknown but he was married in the Friends' Meeting House in 1785. He moved his business to Shipston-on-Stour in Warwickshire, and he died in 1809. Ezra Enock or Enoch (1799–1860) was born in Sibford Gower. From 1827 he traded in Whitechapel in East London, but in 1832 he returned to Sibford Gower where he remained for the rest of his life. His son John Enock (1834–83) traded as a clock repairer in adjoining villages.