Kempster was from Burford in Oxfordshire, England. He sold Cotswold stone from his quarry at Upton, near Burford, to rebuild London after the Great Fire of London in 1666. He was also Christopher Wren's master mason during the rebuilding of St Paul's Cathedral in London. His County Hall built 1678–82 in Abingdon is now the Abingdon County Hall Museum.
His buildings, many with Sir Christopher Wren, include:
- Abingdon County Hall
- St James Garlickhythe, City of London (Kempster also made the font)
- St Mary Abchurch, City of London
- St Mary's Church, North Leigh
- St Stephen Walbrook, City of London
- Tom Tower, Christ Church, Oxford
John Perrott, Lord of the Manor, engaged Kempster to refit St Mary's Church, North Leigh and build a burial chapel for the Perrott family to the north of the north aisle. Kempster linked the Perrott chapel and the north aisle by an arcade of Tuscan columns.
- P.D. Mundy, Chistopher Kempster, Wren's Master-Mason. Notes and Queries, CCII, page 297. Oxford University Press, July 1957. doi:10.1093/nq/CCII.jul.297
- My Family Tree: Jordan, Elizabeth, Rick Bull, 14 November 2007.
- David Nash Ford, Abingdon: Ancient Abbey shaped a Town, Royal Berkshire History.
- Abingdon County Hall: Information for Teachers, English Heritage. Palladian Press, 2004.
- P. Baggs, W.J. Blair, Eleanor Chance, Christina Colvin, Janet Cooper, C.J. Day, Nesta Selwyn, S.C. Townley (1990). Crossley, Alan & Elrington, C.R., eds. Victoria County History: A History of the County of Oxford: Volume 12: Wootton Hundred (South) including Woodstock. Victoria County History of the Counties of England. pp. 231–235. ISBN 0-19-722774-0.
- Seven letters of Wren to John Fell, Bishop of Oxford, and other documents. Published in Wren Society 5 (1928).
- Sherwood, Jennifer; Pevsner, Nikolaus (1974). The Buildings of England: Oxfordshire. Harmondsworth: Penguin Books. pp. 719–720. ISBN 0-14-071045-0.
- Burford, The Cotswold Gateway.